Question

How do you graph the lines using slope-intercept form `h(x) = -x+7`?

Answer 1

graph{-x+7 [-10, 10, -5, 5]}

Explanation:

1) Use the equation and what we know about slope-intercept form to find the slope and y-intercept.

`h(x)=-x+7`

The slope-intercept form equation is: `y=mx+b`

Therefore, the slope (`m`) is `-1` and the y-intercept (`b`) is `7`.

2) Find the *x-intercept*

Set the equation equal to `0` to find the x-intercept

`0=-x+7`
`0-7=-x cancel(+7)-7`
`-7=-x`
`x=7`

So the x-intercept is (7,0)

3) Use what we know to create a graph

• Because of the y-intercept , we know the graph crosses the y-axis at `(0,7)`.
• Because of the x-intercept, we know that the graph crosses the x-axis at `(7,0)`
• Because the slope is negative, we know that the graph is going down.
• Because the slope is rise over run we can use up 1 over 1 to graph a few points and create a line

OR

Create a table or list of coordinates by:

• `x-1`, `y+1` if using the x-intercept. So: `(7,0), (6,1), (5,2),`etc.

or

• `x+1, y-1` if using the y-intercept. So: `(0,7), (1,6), (2,5)`, etc.