Question

What is the equation of the line shown in the graph?

Answer 1

The slope-intercept form:

$y=mx+b$

m - slope

b - y-intercept

The formula of a slope:

$m=\dfrac{y_2-y_1}{x_2-x_1}$

We have the points (-3, 1) and (2, -4). Substitute:

$m=\dfrac{-4-1}{2-(-3)}=\dfrac{-5}{5}=-1$

Therefore we have the equation of a line

$y=-1x+b\to y=-x+b$

Put the coordinates of the point (-3, 1) to the equation:

$1=-(-3)+b$

$1=3+b$      subtract 3 from both sides

$-2=b\to b=-2$

Answer: y = -x - 2