Question

When graphing the inequality y ≤ 2x − 4, the boundary line needs to be graphed first. Which graph correctly shows the boundary line? A. A linear inequalities graph of dotted boundary line intersects X-axis at the unit (2, 0) and Y-axis at the unit (0, minus 4) B. A linear graph of solid line intercepts X-axis at the unit (2, 0) and Y-axis at the unit (0, minus 4) C. A linear inequalities graph of dotted boundary line intercepts at the X-axis (0.5, 0) and Y-axis (0, 2) D. A linear graph of a solid boundary line intersects X-axis at the unit (0.5, 0) and Y-axis at the unit (0, 2)

Answer 1

The correct graph is in the attached image.

Answer 2

B. A linear graph of solid line intercepts X-axis at the point (2, 0) and Y-axis at the point (0, -4)

Explanation:

The boundary line of an inequality is graphed as though the expression were an equality. The nature of the line used will depend on the nature of the inequality.

Form of the line

When the inequality includes the "or equal to" case (≤ or ≥), the boundary line is part of the solution set. It is drawn as a solid line.

When the inequality excludes the "or equal to" case (< or >), the boundary line is not part of the solution set. It is drawn as a dotted or dashed line.

The given inequality

y ≤ 2x -4

includes the "or equal to" case, so the boundary line is solid.

Y-intercept

The equation of the boundary line is written in slope-intercept form:

y = mx +b . . . . . . . line with slope m and y-intercept b

y = 2x -4 . . . . . . . boundary line with slope 2 and y-intercept -4.

This tells you that the boundary line intercepts the y-axis at the point (0, -4).