Question

How do you graph `y\leq - \frac { 8} { 9} x + 2`?

Answer 1

See a solution process below:

Explanation:

First, plot two points where both sides of the inequality are equal:

For `x = 0`: `y = (-8/9 * 0) + 2 = 0 + 2 = 2` or `(0, 2)`

For `x = 9`: `y = (-8/9 * 9) + 2 = -8 + 2 = -6` or `(9, -6)`

graph{(x^2+(y-2)^2-0.125)((x-9)^2+(y+6)^2-0.125)=0[-20, 20, -10, 10]}

Next, draw a line through the two points to mark the boundary of the inequality. Because the equality contains "or equal to" the line will be a solid line. If the inequality was just "less than" it would be a dashed line:

graph{(y+((8/9)x)-2)(x^2+(y-2)^2-0.125)((x-9)^2+(y+6)^2-0.125)=0[-20, 20, -10, 10]}

Now, shade the left side of the line because this is a "less thann or equal to" inequality:

graph{(y+((8/9)x)-2)<=0[-20, 20, -10, 10]}