Which graph best represents all the pairs of numbers (x, y) such that x + y < -6?

Question

Which graph best represents all the pairs of numbers (x, y) such that x + y < -6?

Answer 1

Hi Dana;

We first need to establish the dotted line that represents...

x+y=-6

The line will be dotted because the < is without the = sign and therefore indicates that such is not included in the graph.

I hope you are familiar with < as opposed to >.  In the sixth-grade, we remembered this as, The alligator is going to eat the bigger one.

The equation is in standard form which is...

Ax+By=C, neither A nor B equal zero, and A is greater than zero.

A=1

B=1

C=-6

The slope, change-of-y divided by change-of-x, of the line is...

-A/B=-1/1=-1

We can also establish the slope of the line by converting this from standard form into slope-intercept form.  Slope-intercept form is...

y=mx+b

m is the slope

b is the y-intercept, the value of y when x=0

This will give us enough information.

x + y = -6

Let's subtract x from both sides...

-x+x + y = -x -6

y=-x-6

The slope, m, is -1.

The y-intercept, b, is -6.  This corresponds to point (0,-6).

Begin your dotted line at this point, and move up one unit, and left one unit.

Begin your dotted line at this point, and move down one unit, and right one unit.

Shade the area to the left of (0,-6) because (x+y) is less than that.