Question

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

Answer 1

`y - 2 = -(1)/(3)(x + 3)`

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 = (-1)/(3) = -(1)/(3)`

So the equation of the line is:

`y - 2 = -(1)/(3)(x + 3)`