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

1 Answer
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(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.