How do you graph the inequality #y< -2/5x+1#?

1 Answer
Nov 2, 2015

The slope is #-2/5#.
The y-intercept is #1#. The point is #(0,1)#.
The x-intercept is #2/5#. The point is #(2/5,0)#.

Explanation:

#y<-2/5x+1# is in the slope-intercept form of a linear equation, #y=mx+b#, where #m# is the slope and #b# is the y-intercept. The y-intercept is the value of #y# when #x# is #0#.

Find the #x# and #y# intercepts.

The y-intercept is #+1#.

The point for the y-intercept is #(0,1)#.

Find the #x# intercept by substituting #0# for #y# and solving for #x#.

#0=-2/5x+1#

Subtract #1# from both sides.

#-1=-2/5x#

Multiply both sides by #5#

#5xx-1=-2x#

#-5=-2x#

Divide both sides by #-2#.

#(-5)/(-2)=x#

#5/2=x#

Switch sides.

#x=5/2#

The x-intercept is #5/2#.

The point for the x-intercept is #(5/2,0)#.

Plot the two points on a graph. Draw a straight dashed line through the points to indicate that the line is not part of the inequality. Then shade the area below the line.

graph{y<-2/5x+1 [-10, 10, -5, 5]}