Question

Graph the solution set for this inequality:

[ 4x - 2y > 8 ] also Identify the x- and y-intercepts of the boundary line.
When x = 0, y =
When y = 0, x =

Answer 1

To graph the inequality 4x - 2y > 8, find the intercepts by setting x and y to zero respectively. This gives us points (2,0) for the x-intercept and (0,-4) for the y-intercept. Graph the boundary as a dashed line and shade above the line for the solution set.

Step-by-step explanation:

To graph the solution set for the inequality 4x - 2y > 8, we first consider the corresponding equation 4x - 2y = 8, which represents the boundary line. To find the x-intercept of this line, we set y to 0 and solve for x:

4x - 2(0) = 8 → x = 2.

Thus, when y = 0, x = 2.

To find the y-intercept, we set x to 0 and solve for y:

4(0) - 2y = 8 → -2y = 8 → y = -4.

Thus, when x = 0, y = -4.

Using these intercepts we can sketch the line on a graph. Since the inequality is strict (greater than), we use a dashed line to indicate that points on the line are not included in the solution set. The solution set is the area above the line, as this is where the inequality 4x - 2y > 8 holds true.