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

Feb 1, 2016

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.

$h \left(x\right) = - x + 7$

The slope-intercept form equation is: $y = m x + b$

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 $\left(0 , 7\right)$.
• Because of the x-intercept, we know that the graph crosses the x-axis at $\left(7 , 0\right)$
• 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: $\left(7 , 0\right) , \left(6 , 1\right) , \left(5 , 2\right) ,$etc.

or

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