Question

write an equation in slope intercept form that represents the line shown​

Answer 1

Answer:

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

Step-by-step explanation:

The equation of a line, in slope-intercept is given by:

$y - y_0 = m(x - x_0)$

In which $(x_0,y_0)$ is a point in the line and m is the slope.

We have these following points:

(-3,2), (0,1)

I am going to use $(x_0,y_0) = (-3,2)$

So

$y - 2 = m(x - (-3))$

$y - 2 = m(x + 3)$

Finding the slope

The slope, given two points, is given by the change in y divided by the change in x. In this question:

Points (-3,2) and (0,1).

Change in y: 1 - 2 = -1

Change in x: 0 - (-3) = 0 + 3 = 3

So

$m = \frac{-1}{3} = -\frac{1}{3}$

So the equation of the line is:

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