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

Apr 17, 2018

The slope is $- \frac{1}{2}$ and the y-intercept is $\left(0 , \frac{1}{2}\right)$

#### Explanation:

This equation is in point-slope form which is:

$y - {y}_{1} = m \left(x - {x}_{1}\right)$

m is the slope and $\left({x}_{1} , {y}_{1}\right)$ can be any point on the line. So in this case, the point we are given is $\left(- 3 , 2\right)$

Since there's a $- \frac{1}{2}$ in the m's place for this equation, we automatically know that the slope is $- \frac{1}{2}$ (since m stands for slope).

To find the y-intercept, you'll have to simplify the equation.
Start with distributing the $- \frac{1}{2}$

Given: $y - 2 = - \frac{1}{2} \left(x + 3\right)$

1) Distribute : $y - 2 = - \frac{1}{2} x - \frac{3}{2}$
2) Add 2 to both sides: $y = - \frac{1}{2} x - \frac{3}{2} + 2$
$y = - \frac{1}{2} x + \frac{1}{2}$ <-- equation in standard form

This is the standard form of the equation. From the equation we can see $\frac{1}{2}$ is the y-intercept (plug in 0 for x as y-intercepts always have 0 as the x coordinate) , so your final answer is $\left(0 , \frac{1}{2}\right)$!

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

2) $0 = - \frac{1}{2} x + \frac{1}{2}$ <-- make the equation equal 0 (plug in 0 for y)

3) $- \frac{1}{2} = - \frac{1}{2} x$ <-- subtract both sides by $\frac{1}{2}$

4) $- \frac{1}{2} \div \left(- \frac{1}{2}\right) = x$ <-- divide both sides by $- \frac{1}{2}$

5) $- \frac{1}{2} \cdot \left(- \frac{2}{1}\right) = x$

6)$x = 1$

therefore your answer is $\left(1 , 0\right)$ for the x-intercept.