How to find the slope and y-intercept for y2x<6?

2 Answers
Nov 20, 2017

y<2x+6

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

Explanation:

y2x<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.

y2x<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,

y2x=6

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

y2x=6

y2(0)=6

y=6

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

y2x=6

02x=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=riserun=63=2

![Desmos.com and MS Paint](useruploads.socratic.orguseruploads.socratic.org)

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.

y2x<6

02(0)<6

0<6 is true.

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

![Desmos.com and MS Paint](useruploads.socratic.orguseruploads.socratic.org)