Find the slope and y-intercept of the line is parallel to y=-x-1 and passes through the point (5,-5) *35 points*

10 answers
Question:

Find the slope and y-intercept of the line is parallel to y=-x-1 and passes through the point (5,-5)
*35 points*

Answers

Step-by-step explanation:

y = -x - 1

the slope here is -1. A parallel line will have the same slope

y = mx + b

slope(m) = -1

(5,-5)x = 5 and y = -5

now we subwe are looking for b, the y int

-5 = -1(5) + b

-5 = -5 + b

-5 + 5 = b

0 = b

so ur equation is : y = -x + 0or just y = -x

-2/0 in its simplest form

The slope of the line passing through the points (5, -5) and (7,3) is 4 . Use the slope formula to find the slope.

y = [tex]-\frac{1}{5}[/tex]x - 4

Step-by-step explanation:

Given parameters:

   Coordinates  = (5, -5)

 Equation of the line, x + 5y = 20

Unknown:

Equation of the line parallel to this= ?

Solution:

To find the equation of the line, we must first understand that parallel lines are lines having the same slope. They do not cross each other at any point.

The equation of any straight line is given as;

          y = mx + c

y and x are the coordinates

m is the slope

c is the y- intercept

  Now,

         x + 5y = 20

  Let us find the slope of this line;

            5y  = -x + 20

Divide through by 5;

            y  = [tex]-\frac{1}{5}[/tex]x + 4

The slope of the new line is the coefficient of x;

  Slope =  [tex]-\frac{1}{5}[/tex]

So, let us find the y-intercept of the new line;

          -5 = [tex]-\frac{1}{5}[/tex] x 5 + c

          -5 = -1  + c

           c = -5 + 1   = -4

Now,

    y = [tex]-\frac{1}{5}[/tex]x - 4

-2/0

Step-by-step explanation:

I am pretty sure this is called undefined.

[tex]\large\boxed{y=-\dfrac{1}{3}x-\dfrac{10}{3}\to x+3y=-10}[/tex]

Step-by-step explanation:

The slope-intercept form of an equation of a line:

[tex]y=mx+b[/tex]

m - slope

b - y-intercept

The formula of a slope:

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

We have the points (5, -5) and (-4, -2).

Substiute:

[tex]m=\dfrac{-2-(-5)}{-4-5}=\dfrac{-2+5}{-9}=\dfrac{3}{-9}=-\dfrac{1}{3}[/tex]

Put the value of the slope and the coordinates of the point (5, -5) to the equation of a line:

[tex]-5=-\dfrac{1}{3}(5)+b[/tex]

[tex]-5=-\dfrac{5}{3}+b[/tex]               add 5/3 to both sides

[tex]-\dfrac{15}{3}+\dfrac{5}{3}=b\\\\-\dfrac{10}{3}=b\to b=-\dfrac{10}{3}[/tex]

Finally we have the equation of a line in the slope-intercept form:

[tex]y=-\dfrac{1}{3}x-\dfrac{10}{3}[/tex]

Convert to the standard form (Ax + By = C):

[tex]y=-\dfrac{1}{3}x-\dfrac{10}{3}[/tex]          multiply both sides by 3

[tex]3y=-x-10[/tex]              add x to both sides

[tex]x+3y=-10[/tex]

[tex]slope=\dfrac{\Delta y}{\Delta x}\\\\slope=\dfrac{1}{3}\to\Delta y=1\ and\ \Delta x=3\\\\1\ unit\ up\ and\ 3\ units\ right.\\\\\text{We mark the point (-5, 5). Then move it 1 unit up and 3 units to the right}\\\\Look\ at\ the\ picture.[/tex]


[tex]Graph the line with slope 1/3 passing through the point (5,-5).[/tex]

An equation for the statement is y = -6x + 25.

For this case we have that by definition, the equation of a line of the slope-intersection form is given by:

[tex]y = mx + b[/tex]

Where:

m: It is the slope of the line

b: It is the cut-off point with the y axis

We have the following equation:

[tex]y = -7x + 6[/tex]

With slope [tex]m_ {1} = - 7[/tex]

By definition, if two lines are parallel then their slopes are equal. Thus, a parallel line will be of the form:

[tex]y = -7x + b[/tex]

We replace the point (5,5) through which the line passes and find "b":

[tex]5 = -7 (5) + b\\5 = -35 + b\\5 + 35 = b\\b = 40[/tex]

Finally, the equation is:

[tex]y = -7x + 40[/tex]

On the other hand, if two lines are perpendicular then the product of their slopes is -1. Thus, the slope of a perpendicular line will be:

[tex]m_ {2} = \frac {-1} {m_ {1}} = \frac {-1} {- 7} = \frac {1} {7}[/tex]

Thus, the equation is of the form:

[tex]y = \frac {1} {7} x + b[/tex]

We substitute the point (5, -5) through which the line passes and find "b":

[tex]-5 = \frac {1} {7} (5) + b\\-5 = \frac {5} {7} + b\\-5- \frac {5} {7} = b\\b = \frac {-35-5} {7}\\b = \frac {-40} {7}\\b = - \frac {40} {7}\\[/tex]

Finally, the equation is:

[tex]y = \frac {1} {7} x- \frac {40} {7}[/tex]

[tex]y = -7x + 40\\y = \frac {1} {7} x- \frac {40} {7}[/tex]

it is a

Step-by-step explanation:

Just did it

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