graph ineqiulity

Question

y <= -2x + 3

Answer 1

The inequality is y ≤ - 2x + 3.

The graph of the inequality y ≤ - 2x + 3 is the shaded region, so every point in the shaded region satisfies the inequality.

The graph of the equation y = - 2x + 3 is the boundary of the region. Since the inequality ≤, the boundary is drawn as a solid line to show that points on the line does satisfy the inequality and the shaded region below the graph of y = - 2x + 3.

 

Graph the boundary line by using the x - intercept and y - intercept of the line.

To find the y - intercept, substitute the value of x = 0 in the original equation.

y = - 2(0) + 3 ⇒ y = 3.

The y - intercept is 3, so the graph intersects the y - axis at (0, 3).

 

To find the x - intercept, substitute the value of y = 0 in the original equation.

(0) = - 2x + 3 ⇒ x = 3/2 = 1.5.

The x - intercept is 1.5, so the graph intersects the x - axis at (1.5, 0).

 

To draw inequality y ≤ - 2x + 3 follow the steps.

1.  Draw a coordinate plane.

2.  Plot the points and draw a line through these points.

3.  To determine which half-plane to be shaded use a test point in either half-plane. A simple choice is (0, 0).

Substitute the value of (x, y) = (0, 0) in the original inequality.

(0) ≤ - 2(0) + 3 ⇒ 0 ≤ 3.

4.  Since the above statement is true, shade the region that contains point (0, 0).

The inequality y ≤ - 2x + 3 graph is