How do you graph $y = - \frac{1}{2} x - 5$ $y=-1/2x-5$ using intercepts?

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Answer 1 · 2017-04-26T16:41:20

x-intercept: $(- 10, 0)$ $( -10, 0 )$
y-intercept: $(0, - 5)$ $( 0 , -5 )$

To start off, we know that intercepts only exist when the x-coordinate or y-coordinate of a point equal 0.

So we look into the given function:

$y = - \frac{1}{2} x - 5$ $y = -1/2x - 5$

To find the y-intercept, the x-coordinate has to equal 0, so let's plug in 0 into the function.

$y = - \frac{1}{2} \cdot 0 - 5$ $y = -1/2*0 - 5$

$y = - 5$ $y = - 5$

So now we know when $x = 0$ $x = 0$ , $y = - 5$ $y = -5$ . So we have a point $(0, - 5)$ $( 0 , -5 )$ on the graph.

For the x-intercept, the y-coordinate has to equal 0. We plug it in to get:

$0 = - \frac{1}{2} x - 5$ $0 = -1/2x - 5$

$\frac{1}{2} x = - 5$ $1/2x = -5$

$x = - 10$ $x = -10$

So we now have the x intercept at point $(- 10, 0)$ $( -10, 0 )$

Here's a graph for reference:

graph{y = -1/2x-5 [-13, 7, -6.96, 3.04]}

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