Question

How do you find the slope and intercept to graph `y-2=-1/2(x+3)`?

Answer 1

The slope is `-1/2` and the y-intercept is `(0,1/2)`

Explanation:

This equation is in point-slope form which is:

`y-y_1= m (x-x_1)`

m is the slope and `(x_1,y_1)` can be any point on the line. So in this case, the point we are given is `(-3,2)`

Since there's a `-1/2` in the m's place for this equation, we automatically know that the slope is `-1/2` (since m stands for slope).

To find the y-intercept, you'll have to simplify the equation.
Start with distributing the `-1/2`

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

1) Distribute : `y-2= -1/2x-3/2`
2) Add 2 to both sides: `y= -1/2x-3/2 +2`
`y= -1/2x+1/2` <-- equation in standard form

This is the standard form of the equation. From the equation we can see `1/2` is the y-intercept (plug in 0 for x as y-intercepts always have 0 as the x coordinate) , so your final answer is `(0,1/2)`!

I'm not sure if you wanted to find what the x-intercept is as well but I'll tell you how to do that too.

x-intercepts always have a 0 in the y coordinate so make the equation equal to 0/plug in 0 for y.

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

2) `0= -1/2x+1/2` <-- make the equation equal 0 (plug in 0 for y)

3) `-1/2= -1/2x` <-- subtract both sides by `1/2`

4) `-1/2-: (-1/2)= x` <-- divide both sides by `-1/2`

5) `-1/2 *(-2/1)= x`

6)`x=1`

therefore your answer is `(1,0)` for the x-intercept.