Question

Write the slope-intercept inequality for the graph below (3,2) (-3,-6).

Answer 1

Let the points are (x₁, y₁) = (3, 2) and (x₂, y₂) = (- 3, - 6).

Slope m = [(y₂ - y₁)/(x₂ - x₁)]

m = [(- 6 - 2)/(- 3 - 3)]

m = 8/6

m = 4/3.

To find the y - intercept, substitute the values of (x, y ) = (3, 2) and m = 4/3 in the slope - intercept from of equation y = mx + b and solve for b.

2 = 4/3 * 3 + b

b = - 4 + 2 = - 2.

Substitute the values of m = 4/3 and b = - 2 in the slope - intercept form of equation.

y = mx + b ⇒ y = (4/3)x - 2.

From the given data slope - intercept inequality for th graph brlow (3, 2) and (- 3, - 6) is

y < (4/3)x - 2.

Graph of the inequality :

The graph of the inequality y < (4/3)x - 2 symbol is <, the boundary is not included in the solutionset. Graph the boundary of the inequality y = (4/3)x - 2 with dotted line.

1. Draw the coordinate plane.

2. To determine which half - plane to be shaded use a test point in either half - plane.

A simple choice is (0, 0).

Substitute x = 0 and y = 0 in the inequality y < (4/3)x - 2.

0 < (4/3)0 - 2

0 < - 2.

The above statement is false.

3. Since the statement is false, shade the region does not contains point (0, 0).