Write y = 1/6x + 5 in standard form using integers.

9 answers
Question:

Write y = 1/6
x + 5 in standard form using integers.

Answers

# 1 is d
# 2 is d
# 3 is b

1. d
x-intercept (y=0) is -4
y-intercept (x=0) is 8

2. d
x-intercept (y=0) is 16
y-intercept (x=0) is 20

3. b
y=1/6x+4
multiplied by 6
6y=x+24
-x+6y=24

4. a 4.75k+2.25p=22

1. For the data in the table, does y vary directly with X? If it does write an equation for the direct variation.(X,y) (8,11) (16,22) (24,33) 

Yes y=1.375x 

2.for the data in the table, does y vary directly with X? If it does write an equation for the direct variation. (X,y) (16,4) (32,16) (48,36) 
No y does not very directly with x***  

3. (Time/hour,distance/miles)(4,233) (6,348) (8,464) (10, 580) 
Express the relationship between distance and time in a simplified form as a unit rate. Determine which statement correctly interprets this relationship. 
58/1 your car travels 58 miles in 1 hour 

4.what is the slope of the line that passes through the pair of points (2,5) and (8,3) 

-1/3 

4.what is the slope of the line that passes through the pair of points (-5.2,8.7) and (-3.2,2.7) 

-3 

5. What is the slope of the line that passes through the pair of points (3/2,-2) and (-3,7/3) 

-26/27 

6.write an equation in point slope from for the line through the given point with the given slope (5,2) m=3 
 
Y-2=3(X-5) 

7. Write an equation in point slope form for the line through the given point with the given slope (-3,-5) m=-2/5 

Y+5=-2/5(X+3) 

8. Write an equation in point slope from for the line through the given point with the given slope. (4,-7) m=-0.54 

Y+7=-0.54(x-4) 

9. The table shows the height of a plant as it grows. Which equation in point slope from gives the plants height (time,plant height) (2,16)(4,32)(6,48)(8,64) 

Y-16=8(X-2)*** 

10. Write y=-2/3x+7 in standard form

2x+3y=21 

11. Write y=-1/2x+1 in standard form using integers 

X+2y=2 

1=b
i will finish this when i get home for you

1. d. x-intercept is -4; y-intercept is 8.

2.d. x-intercept is 16; y-intercept is 20

3. b. -x+6y=24

4.  a. 4.75k+2.25p=22

Step-by-step explanation:

1. -10x+5y=40

to find the y intercept   let x =0

5y = 40

divide by 5

y = 40/5  = 8

to find the x intercept   let y =0

-10x = 40

divide by -10

x = 40/-10

x=-4


2. 5x+4y=80

to find the y intercept   let x =0

4y = 80

divide by 4

y = 80/4  = 20

to find the x intercept   let y =0

5x = 80

divide by 5

x = 80/5  

x=16


3. Write y=1/6x+4 in standard form using integers.

Ax+by =c

multiply each side by 6

6y = 6* (1/6 x + 4)

6y = x+24

subtract x from each side

-x+6y = x-x+24

-x +6y = 24


4. lbs of kumquats * price/per + lbs of pears * price/lb =22

 k * 4.75 + p * 2.25 =22

4.75k + 2.75p = 22

1. D

2. D

3. B

4. A

5. D

Step-by-step explanation:

hope it helps. :)

1. Option D.

2. Option D.

3. Option B.

4. Option A.

5. The graph of x=-2 is shown below.

Step-by-step explanation:

1.

The given equation is

[tex]-10x + 5y = 40[/tex]

Substitute x=0, to find the y-intercept.

[tex]-10(0) + 5y = 40\Rightarrow 5y=40\Rightarrow y=8[/tex]

Substitute y=0, to find the x-intercept.

[tex]-10x + 5(0) = 40\Rightarrow -10x=40\Rightarrow x=-4[/tex]

Since x-intercept is -4; y-intercept is 8, therefore the correct option is D.

2.

The given equation is

[tex]5x + 4y = 80[/tex]

Substitute x=0, to find the y-intercept.

[tex]5(0) + 4y = 80\Rightarrow 4y=80\Rightarrow y=20[/tex]

Substitute y=0, to find the x-intercept.

[tex]5x + 4(0) = 80\Rightarrow 5x=80\Rightarrow x=16[/tex]

Since x-intercept is 16; y-intercept is 20, therefore the correct option is D.

3.

The given equation is

[tex]y=\frac{1}{6}x+4[/tex]

Standard form of a line is ax+bx=c.

Multiply both sides by 6.

[tex]6y=x+24[/tex]

Subtract x from both sides.

[tex]-x+6y=24[/tex]

Therefore, the correct option is B.

4.

Let k be the weights of kumquats and p be the weights of Asian pears.

A grocery store sells kumquats for $4.75 a pound and Asian pears for $2.25 a pound.

Total cost = 4.75k + 2.25p

Customer could buy for $22.

[tex]4.75k + 2.25p=22[/tex]

Therefore, the correct option is A.

5.

The given equation is

[tex]x=-2[/tex]

We need to find the graph of given equation.

We know that x=a is a vertical line which passes through the point (0,a).

The given equation x=-2 is a vertical line which passes through the point (0,-2).

The graph of x=-2 is shown below.


[tex]Me! for questions 1-2 find the x- and y-intercept of the line. 1. -10x + 5y = 40 a. x-intercept is[/tex]

1. y varies directly with x and the equation is  [tex]y=1.375x[/tex]

2. No, y does not vary directly with x

3. Your car travels 58 miles in 1 hour

4. [tex]-\frac{1}{3}[/tex]

4. [tex]-3[/tex]

5. [tex]-\frac{26}{27}[/tex]

6. [tex]y-2=3(x-5)[/tex]

7. [tex]y+5=-\frac{2}{5}(x+3)[/tex]

8. [tex]y+7=-0.54(x-4)[/tex]

9. [tex]y-16=8(x-2)[/tex]

10. [tex]2x+3y=21[/tex]

11. [tex]x+2y=2[/tex]


Step-by-step explanation:


1.

For [tex]y[/tex] to vary directly with [tex]x[/tex] , all the 3 pair of numbers need to show the same ratio if we divide each y's by the x's. Let's check.

[tex]\frac{11}{8}=1.375[/tex][tex]\frac{22}{16}=1.375[/tex][tex]\frac{33}{24}=1.375[/tex]

So all of them show the same ratio and hence y varies directly with x.

For equation, we already saw that multiplying x by 1.375 gives us y. We can write in equation form as:

[tex]y=1.375x[/tex]

Third answer choice is correct.


2.

This is similar to #1. So let's check the ratios.

[tex]\frac{4}{16}=0.25[/tex][tex]\frac{16}{32}=0.5[/tex][tex]\frac{36}{48}=0.75[/tex]

As we can see, the ratios are not equal to y does not vary directly with x.

Fourth answer choice is correct.


3.

The first number in the pair gives time and second number gives distance. To get unit rate, we divide the distance by time. So we will get the number of miles traveled in 1 hour.

[tex]\frac{233}{4}=58.25[/tex]  [ i believe this is a typo and it should be 232 miles and ratio would be 58 ]

[tex]\frac{348}{6}=58[/tex]

[tex]\frac{464}{8}=58[/tex]

[tex]\frac{580}{10}=58[/tex]

As we can see, in 1 hour, distance covered is 58 miles. Third answer choice is right.


4.

If the 2 points are taken as  [tex](x_{1},y_{1})[/tex]  and  [tex](x_{2},y_{2})[/tex]

And we know formula of slope to be:

[tex]\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]

The slope of the line is:

[tex]\frac{3-5}{8-2}=\frac{-2}{6}=-\frac{1}{3}[/tex]

The slope of the line is  [tex]-\frac{1}{3}[/tex]

Second answer choice is correct.


4. [this should be #5]

If the 2 points are taken as  [tex](x_{1},y_{1})[/tex]  and  [tex](x_{2},y_{2})[/tex]

And we know formula of slope to be:

[tex]\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]

The slope of this line can be found now:

[tex]\frac{2.7-8.7}{-3.2-(-5.2)}=\frac{2.7-8.7}{-3.2+5.2}=\frac{-6}{2}=-3[/tex]

The slope of the line is  [tex]-3[/tex]

Fourth answer choice is correct.


5.

The formula of slope is:

[tex]\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]

Where,

the 2 points are taken as  [tex](x_{1},y_{1})[/tex]  and  [tex](x_{2},y_{2})[/tex]

Now finding the slope:

[tex]\frac{\frac{7}{3}-(-2)}{-3-\frac{3}{2}}=\frac{\frac{7}{3}+2}{-\frac{9}{2}}=\frac{\frac{13}{3}}{-\frac{9}{2}}=-\frac{26}{27}[/tex]

The slope of the line is  [tex]-\frac{26}{27}[/tex]

Second answer choice is right.


6.

Point Slope form of a line is given as:

[tex]y-y_{1}=m(x-x_{1})[/tex]

Where,

[tex](x_{1},y_{1})[/tex] is the point given, andm is the slope

Using the point (5, 2) and slope as 3 given, we can write the equation:

[tex]y-2=3(x-5)[/tex]

Fourth answer choice is right.


7.

Point Slope form of a line is given as:

[tex]y-y_{1}=m(x-x_{1})[/tex]

Where,

[tex](x_{1},y_{1})[/tex] is the point given, andm is the slope

Using the point given as  [tex](-3,-5)[/tex] and slope as [tex]m=-\frac{2}{5}[/tex] , we can write the point slope form of the equation as:

[tex]y-(-5)=-\frac{2}{5}(x-(-3))\\y+5=-\frac{2}{5}(x+3)[/tex]

First answer choice is right.


8.

Point Slope form of a line is given as:

[tex]y-y_{1}=m(x-x_{1})[/tex]

Where,

[tex](x_{1},y_{1})[/tex] is the point given, andm is the slope

The slope is given as [tex]-0.54[/tex] and the point is (4, -7). So the point slope form is:

[tex]y-(-7)=-0.54(x-4)\\y+7=-0.54(x-4)[/tex]

First answer choice is right.


9.

In this question, we can just have a quick look and see that the [tex]y[/tex]-coordinate is 8 times the [tex]x[/tex]-coordinate. So we can say that [tex]y=8x[/tex]

Expanding the equations below would tell us which one is equal to that. Let's check.

[tex]y-16=8(x-2)\\y-16=8x-16\\y=8x-16+16\\y=8x[/tex]

This is the correct one.

So first answer choice is right.


10.

The standard form of the equation of a line is given as:

[tex]Ax+By=C[/tex]

Rearranging the given equation gives us:

[tex]y=-\frac{2}{3}x+7\\\frac{2}{3}x+y=7[/tex]

Now, we can't have a fraction, so we multiply all of it by 3 to get rid of the denominator. Now we have:

[tex]3*(\frac{2}{3}x+y=7)\\2x+3y=21[/tex]

First answer choice is right.


11.

The standard form of a line is  [tex]Ax+By=C[/tex]

Rearranging the given equation, we have:

[tex]y=-\frac{1}{2}x+1\\\frac{1}{2}x+y=1[/tex]

We cannot have fractions, so we multiply the whole thing by 2 to get rid of the denominator. So we have:

[tex]2*(\frac{1}{2}x+y=1)\\x+2y=2[/tex]

First answer choice is correct.

Part 1) x-intercept is -4;y-intercept is 8

Part 2) x-intercept is 16; y-intercept is 20

Part 3) [tex]x+6y=24[/tex]

Part 4)

Part a) [tex]4.75k+2.25p=22[/tex]

Part b) The graph in the attached figure

Step-by-step explanation:

Part 1) Find the x- and y-intercept of the line

we have

[tex]-10x+5y = 40[/tex]

we know that

The x-intercept is the value of x when the value of y is equal to zero

so

For y=0

[tex]-10x+5(0) = 40[/tex]

[tex]-10x=40[/tex]

[tex]x=-4[/tex]

The y-intercept is the value of y when the value of x is equal to zero

so

For x=0

[tex]-10(0)+5y = 40[/tex]

[tex]5y = 40[/tex]

[tex]y=8[/tex]

therefore

x-intercept is -4;y-intercept is 8

Part 2) Find the x- and y-intercept of the line

we have

[tex]5x+4y=80[/tex]

we know that

The x-intercept is the value of x when the value of y is equal to zero

so

For y=0

[tex]5x+4(0)=80[/tex]

[tex]5x=80[/tex]

[tex]x=16[/tex]

The y-intercept is the value of y when the value of x is equal to zero

so

For x=0

[tex]5(0)+4y=80[/tex]            

[tex]4y=80[/tex]

[tex]y=20[/tex]              

therefore

x-intercept is 16; y-intercept is 20

Part 3) Write y=-(1/6)x+4 in standard form using integers.

we know that

The equation of a line in standard form is equal to

[tex]Ax+By=C[/tex]

where

A is a positive integer

B and C are integers

we have

[tex]y=-\frac{1}{6}x+4[/tex]

Multiply both sides by 6 to remove the fraction

[tex]6y=-x+24[/tex]

Adds x both sides

[tex]x+6y=24[/tex]

Part 4) The grocery store sells kumquats for $4.75 a pound and Asian pears for $2.25 a pound.

Part a) Write an equation in standard form for the weights of kumquats k and Asian pears p that a customer could buy with $22

Part b) Graph the equation

Part a)

Let

k -----> the number of pounds of kumquats bought

p ----> the number of pounds of Asian pears bough

we know that

The number of pounds of kumquats bought (k) multiplied by it cost of $4.75 a pound plus the number of pounds of Asian pears bough (p) multiplied by it cost of $2.25 a pound must be equal to $22

so

[tex]4.75k+2.25p=22[/tex]

Part b) Graph the equation

To graph the line find out the intercepts

Let

k the first coordinate of the point

p the second coordinate of the point

The k-intercept is the value of k when the value of p is equal to zero

so

For p=0

[tex]4.75k+2.25(0)=22[/tex]

[tex]4.75k=22[/tex]

[tex]k=4.63[/tex]

so

The k-intercept is the point (4.63,0)

The p-intercept is the value of p when the value of k is equal to zero

so

For k=0

[tex]4.75(0)+2.25p=22[/tex]

[tex]2.25p=22[/tex]

[tex]p=9.78[/tex]

so

The k-intercept is the point (0,9.78)

using a graphing tool

Plot the intercepts and join the points to graph the line

see the attached figure

Remember that the weight cannot be a negative number


[tex]2for question 1, find the x- and y-intercept of the line.1. -10x+5y = 40 (1 point)x-intercept is 5;[/tex]

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