How to find the slope and y-intercept for y-2x<6?

2 Answers
Nov 20, 2017

y<2x+6

The slope is 2 and the y-intercept is 6.

Explanation:

y-2x<6

Solve for y to get the inequality into slope-intercept form:

y=mx+b,

where:

m is the slope, and b is the y-intercept.

Solve for y.

y-2x<6

Add 2x to both sides.

y<2x+6

The slope is 2 and the y-intercept is 6.

Nov 20, 2017

y-intercept: (0, 6)
Slope: m=2
The solution for y is given by the graph below.

Explanation:

The easiest way to evaluate this inequality is to pretend (for a moment) that we are actually dealing with the equation,

y-2x = 6

The y intercept of an equation occurs when x=0.

y-2x = 6

y-2(0) = 6

y = 6

So the y-intercept is the point (0, 6). The x-intercept occurs when y=0.

y - 2x = 6

0 - 2x = 6

-2x = 6

x = -3

So the x-intercept is the point (-3, 0). Draw a dashed line through these points to account for the inequality symbol.

The slope is the rise over the run.

m="rise"/"run"=6/3=2

Desmos.com and MS PaintDesmos.com and MS Paint

The final step is to determine where to shade by choosing an easy point, like (0, 0). If plugging in this point makes the original inequality a true statement, then shade that entire side of the line.

y-2x<6

0-2(0)<6

0 < 6 is true.

So shade the side with the point (0, 0)

Desmos.com and MS PaintDesmos.com and MS Paint