What is the equation of the graphed line in point-slope form? y – 1 = 2/3 (x + 3), y – 1 = 2/3 (x – 3), y + 1 = 2/3

8 answers
Question:

What is the equation of the graphed line in point-slope form? y – 1 = 2/3 (x + 3), y – 1 = 2/3 (x – 3), y + 1 = 2/3 (x – 3), y + 1 = 2/3 (x + 3) (points are at (-3,-3) and (3,1)

Answers

Hello!

First of all we need to find the slope. To do so we use the following equation.

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

The ones and twos just represent different ordered pairs. We will have (-3,3) be ([tex]x_{1} , y_{1}[/tex]) and (3,1) be ([tex]x_{2} , y_{2}[/tex]) Now we plug our numbers into the formula.

[tex]\frac{1+3}{3+3} = \frac{4}{6} = \frac{2}{3}[/tex]
---------------------------------------------------
Now we need to write our equation in point-slope form, which is y-k=m(x-h), where (h,k) represent a point on the line, and m is the slope.. We will use (3,1) for (h,k). Our final equation is shown below.

y-1= [tex]\frac{2}{3}[/tex](x+3)

I hope this helps!

(3,1)(-3,-3)
slope = (-3 - 1) / (-3 - 3) = -4/-6 = 2/3

y - y1 = m(x - x1)
slope(m) = 2/3
(3,1)x1 = 3 and y1 = 1
now sub
y - 1 = 2/3(x - 3) <===

b

Step-by-step explanation:

ANSWER

[tex]y - 1 = \frac{2}{3} (x - 3)[/tex]

EXPLANATION

To find the equation in point-slope form, use the formula,

[tex]y-y_1=m(x-x_1)[/tex]

The [tex]m[/tex]
is the slope of the line.

We can read from the graph that, the straight line passes through, the points
[tex](-3,-3) \: and \: (3,1)[/tex]

We can use these two points to find the slope of the line.

The slope can found using the formula,

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

This means that,

[tex]m = \frac{1 - - 3}{3 - - 3}[/tex]

[tex]m = \frac{1 + 3}{3 + 3}[/tex]

[tex]m = \frac{4}{6}[/tex]

[tex]m = \frac{2}{3}[/tex]

We now use one of the points, say
[tex](3,1)[/tex]
with the slope to find the equation of the line.

[tex]y - 1 = \frac{2}{3} (x - 3)[/tex]

ANSWER

[tex]y - 1 = \frac{2}{3} (x - 3)[/tex]

EXPLANATION

To find the equation in point-slope form, use the formula,

[tex]y-y_1=m(x-x_1)[/tex]

The [tex]m[/tex]
is the slope of the line.

We can read from the graph that, the straight line passes through, the points
[tex](-3,-3) \: and \: (3,1)[/tex]

We can use these two points to find the slope of the line.

The slope can found using the formula,

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

This means that,

[tex]m = \frac{1 - - 3}{3 - - 3}[/tex]

[tex]m = \frac{1 + 3}{3 + 3}[/tex]

[tex]m = \frac{4}{6}[/tex]

[tex]m = \frac{2}{3}[/tex]

We now use one of the points, say
[tex](3,1)[/tex]
with the slope to find the equation of the line.

[tex]y - 1 = \frac{2}{3} (x - 3)[/tex]

First you do the distributive property and then you have to use the inverse property of each equation and after all the math the answer is y-1= 2/3(x-3)

P.S: Next time you may want to add the fractions in the possible answers

Slope = 4/6= 2/3
Intercept is -1 (I think just check with gradient on graph in doing in my head)

Y=MX+B
Y=2/3X-1 ( if my calculations add up

We first need to find the gradient of the line
[tex]\frac{y_{2}- y_{1} } {x_{2}-x_{1} } = \frac{-3-1}{-3-3}= \frac{-4}{-6}= \frac{2}{3}[/tex]

From the graph, we see the graph intercepts y-axis at -1

Hence, the equation of the line is [tex]y= \frac{2}{3}x-1[/tex]

Similar Solved Works

1 answer

A band expects to put 15 songs on their next CD. The band writes and records 60% more songs than they expect to put on the

A band expects to put 15 songs on their next CD. The band writes and records 60% more songs than they expect to put on the CD. During the editing process, 12.5% of the songs are removed. How many songs will there be on the final CD?​...
2 answers

At a peanut plant, a 3oz bag of unshelled peanuts should contain 105 peanuts. The machine that fills

At a peanut plant, a 3oz bag of unshelled peanuts should contain 105 peanuts. The machine that fills the bags counts the peanuts as they are put into the bag. The machine has a tolerance of 3 peanuts over or under the goal of 105. Fill in the parts of the absolute value that are missing to make an ...
3 answers

Where can you hear a language composed of only whistling sounds?

Where can you hear a language composed of only whistling sounds?...
12 answers

Please help me ill give you the crown thing if its right

Please help me ill give you the crown thing if its right [tex]Please help me ill give you the crown thing if its right[/tex]...
3 answers

The area of a rectangular ceiling tile is 234 square inches. the perimeter is 62 inches. what are the

The area of a rectangular ceiling tile is 234 square inches. the perimeter is 62 inches. what are the dimensions of the tile?...
12 answers

3.2 Write the following ratio in their simplest form.a) 150 minutes : 2 hoursb) 150 cm : 1060 mm3.3 A student is paid R75,00 for a 6

3.2 Write the following ratio in their simplest form. a) 150 minutes : 2 hoursb) 150 cm : 1060 mm3.3 A student is paid R75,00 for a 6 hour shift as a wait​...
3 answers

Why did the americans in the western part of the country support the war?

Why did the americans in the western part of the country support the war?...
1 answer

Aqua Corporation purchases nonresidential real property on May 8, 2015, for $1,000,000. Straight-line cost recovery is taken

Aqua Corporation purchases nonresidential real property on May 8, 2015, for $1,000,000. Straight-line cost recovery is taken in the amount of $89,765 before the property is sold on November 30, 2018, for $1,500,000 a. Compute the amount of Aqua's recognized gain on the sale of the realty 17,953 X Fe...
12 answers

This is Urgent please help!!

This is Urgent please help!! [tex]This is Urgent please help!![/tex]...
3 answers

Answer the question from the attachment.

Answer the question from the attachment. [tex]Answer the question from the attachment.[/tex]...
12 answers

4. What is the measure of angle ABD in the figure below?*D2xABс

4. What is the measure of angle ABD in the figure below?* D 2x A B с...
2 answers

What is the mass of 3.00 moles of magnesium chloride, mgcl2? express your answer with the appropriate units.

What is the mass of 3.00 moles of magnesium chloride, mgcl2? express your answer with the appropriate units....
2 answers

According to the following reaction, how many grams of sulfur are formed when 37.4 g of water are formed?2

According to the following reaction, how many grams of sulfur are formed when 37.4 g of water are formed? 2 H2S(g) + SO2(g) → 3 S(s) + 2H2O(l)...
3 answers

The ratio of leopard coats to mink stoles is 3 to 19 if there are 76 mink stoles how many leopard coats

The ratio of leopard coats to mink stoles is 3 to 19 if there are 76 mink stoles how many leopard coats are there...
3 answers

5. Why is the scene at the camera store ironic?a. The narrator was unaware of a crucial part of his father's past.b. The narrator

5. Why is the scene at the camera store ironic? a. The narrator was unaware of a crucial part of his father's past. b. The narrator believed that his father was an important person. c. The narrator failed to believe in his father's self-confidence. d. The narrator assumed that his father was highl...
4 answers

Battle of the trees video worksheet answers

Battle of the trees video worksheet answers...
3 answers

You have 3/6 a cup of oatmeal in your cupboard. A recipe for cookies calls for 1/4 cup of oatmeal. How much oatmeal would you have left

You have 3/6 a cup of oatmeal in your cupboard. A recipe for cookies calls for 1/4 cup of oatmeal. How much oatmeal would you have left if you made the cookies?​...
4 answers

What does Sertaline do? ASAP!!!

What does Sertaline do? ASAP!!!...
7 answers

Behrgan and McKenna are riding bikes around the neighborhood loop. It takes Behrgan 2.4 minutes to get

Behrgan and McKenna are riding bikes around the neighborhood loop. It takes Behrgan 2.4 minutes to get around the loop and McKenna 1.6 minutes. If they both start riding from the same spot at the same time, when do they meet at the start spot again. Please Explain...
4 answers

The Essay question: What ideas caused the institution of slavery to be supported? Your response will be the thesis, or what you are trying

The Essay question: What ideas caused the institution of slavery to be supported? Your response will be the thesis, or what you are trying to prove....

-- 0.054103--