Question

What is the equation of the line on the graph? Write your answer in slope-intercept form. (y = mx + b)

Answer 1

Answer:

y= ⅔x -2

Step-by-step explanation:

slope-intercept form

y= mx +b, where m is the slope and b is the y-intercept.

Two given coordinates: (-3, -4) and (6, 2)

$\boxed{slope = \frac{y1 - y2}{x1 - x2} }$

Slope

$= \frac{2 - ( - 4)}{6 - ( - 3)}$

$= \frac{2 + 4}{6 + 3}$

$= \frac{6}{9}$

$= \frac{2}{3}$

Substitute m= ⅔ into the equation:

y= ⅔x +b

From the graph, the y- intercept is -2 since the line cuts through the x-axis at (0, -2).

Alternatively, we can also substitute a pair of coordinates into the equation to find the value of b.

When x= 6, y= 2,

$2 = \frac{2}{3} (6) + b$

2= 4 +b

b= 2 -4

b= -2

Thus the equation of the line is y= ⅔x -2.