Lesson 7: Graphs of linear systems and inequalities

Where on the graph is the solution for both of these equations?

The point where both lines intersect

When do you draw a solid line on a graph when graphing an inequality?

When the inequality has a greater/less than or equal to sign

When do you draw a dashed line on a graph when graphing an inequality?

When the inequality has a > or < sign (no equal to) OR if any points above that line is not a solution to the line

How do you graph the infinite number of (x, y) values that can satisfy a linear equation?

You shade the xy-plane

How do you know which half of the xy-plane to shade when graphing?

Look at the sign in the inequality

Do you shade above or below the line if y is greater than mx+b?

Above

Do you shade above or below the line if y is less than mx+b?

Below

How would you draw y > x on a graph? (aka what line you use and where you shade)

Dotted line, shading above line

How would you draw y is less than or equal to x on a graph? (aka what line you use and where you shade)

Solid line, shading below line

The point (1, 1) is (inside/outside) the shaded area, so it (is/is not) a solution to the inequality

Inside, is

The point (-3, -4) is (inside/outside) the shaded area, so it (is/is not) a solution to the inequality

Outside, is not

Another line intersects this inequality. Would the points in THIS inequality be solutions to the other line?

No

What color shaded region on the graph do the points satisfy BOTH inequalities?

Blue region

What is the point slope form?

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

The graph of a line in the xy-plane has a slope of 3 and passes through the origin. The graph of a second line has a slope of 6 and passes through the point (-1, -9). If the two lines intersect at the point (a, b), what is the value of a?

a = 1