Question

How do you graph `y=-1/2x-5` using intercepts?

Answer 1

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

Explanation:

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 = -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 = -1/2*0 - 5`

`y = - 5`

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

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

`0 = -1/2x - 5`

`1/2x = -5`

`x = -10`

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

Here's a graph for reference:

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