Question

*100 POINTS* *100 POINTS*

Answer 1

Answer:

$\huge{ \boxed{y = - \frac{1}{3} x + 1}}$

Step-by-step explanation:

Equation of a line is y = mx + c

where

m is the slope

c is the y intercept

From the graph to find the equation of the line we must first find the slope

The slope of a line given two points can be found by using the formula

$m = \frac{ y_2 - y _ 1}{x_ 2 - x_ 1}$

where

(x1 , y1) and (x2 , y2) are the points

Using the points (-6 , -3) and (6,-7) we have

$m = \frac{ - 7 - - 3}{6 - - 6} = - \frac{4}{12} = - \frac{1}{3}$

Next we use the slope that has been found and one of the points to find the equation of the line

To find an equation of a line when given the slope and a point we use the formula

y - y1 = m(x - x1)

where

m is the slope

( x1 , y1) is the point

From the question using slope -1/3 and point (-6,3) we have

$y - 3 = - \frac{1}{3} (x - - 6) \\ y - 3 = - \frac{1}{3} (x + 6) \\ y - 3 = - \frac{1}{3} x - 2 \: \: \: \\ y = - \frac{1}{3} x - 2 + 3 \: \:$

The equation of the line in slope-intercept form is

$y = - \frac{1}{3} x + 1$

Hope this helps you

Answer 2

Answer:

• y = - 1/3x - 5

Step-by-step explanation:

Use two given points (-6, -3) and (6, -7) to find equation of the line.

The slope:

• m = (y₂ - y₁)/(x₂ - x₁) = (-7 - (-3)) / (6 - (-6)) = -4 / 12 = - 1/3

The y - intercept is also visible on the graph (0, -5):

• b = -5

The line is:

• y = - 1/3x - 5