Question

Match the correct y=mx+b equation to the graph: pls show work/explanation!

Answer 1

Answer:

$\displaystyle y=\frac{1}{3}x-2$

$\displaystyle m=\frac{1}{3},\ b=-2$

Step-by-step explanation:

Equation of a line

We only need two points through which it passes to define the equation of a line. The graph provided in the question shows two clear points to pick: (0,-2) and (3,-1)

Now we wet up the equation of the line by using the formula

$\displaystyle y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)$

Plugging in the points:

$\displaystyle y-(-2)=\frac{-1-(-2)}{3-0}(x-0)$

Operating

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

$\displaystyle y=\frac{1}{3}x-2$

The values of m and b are

$\displaystyle \boxed{m=\frac{1}{3},\ b=-2}$