Write an inequality whose graph is described by the given information. The points (−7,−16) and (1, 8) lie on the boundary line. The points (−7, 0) and (3, 14) are not solutions of the inequality.

Question

(-7,16)

(1,8)

on boundary line

(-7,0)

(3,14)

not on boundary line

Answer 1

I can find the equation for this. But cannot tell based on how the problem is worded is the points that lie on the boundary line are a part of the solution or not.

First, find the slope using the points on the boundary line.

m=(y2-y1)/(x2-x1)

m=(8-(-16))/(1-(-7)

m=(8+16)/(1+7)

m=24/8

m=3

Next, you can use this formula and plug in the slope and one of the points rrom the boundary line

(y-y1)=m(x-x1)

(y-8)=3(m-1) Distribute

y-8=3m-3 Add 8 to both sides

y-8+8=3m-3+8

y=3m+5

I sketched the equation and the points that were not a part of the solution. It looked like the inequalities should be less than. So I tested it out to confirm. The points should give a false statement.

y<3x+5

0<3(-7)+5

0<-21+5

0<-16 is false, so the equation is correct.

y<3x+5 if the boundary points are NOT a part of the solution

y≤3x+5 if the boundary points ARE a part of the solution