Question

a coordinate plane with two straight lines, both increasing from left to right, with one line intersecting the x-axis at -2 and the y-axis at 2, and the other line intersecting the x-axis at 4 and the y-axis at -4. which statement about these lines is true? the lines are perpendicular because they will never touch or intersect. the lines are parallel because they intersect at a 90° angle. the lines are perpendicular because they intersect at a 90° angle. the lines are parallel because they will never touch or intersect.

Explanation:

Step1: Find slopes of both lines

For the first line, x-intercept \((-2, 0)\) and y-intercept \((0, 2)\). Slope \(m_1=\frac{2 - 0}{0 - (-2)}=\frac{2}{2}=1\).
For the second line, x-intercept \((4, 0)\) and y-intercept \((0, -4)\). Slope \(m_2=\frac{-4 - 0}{0 - 4}=\frac{-4}{-4}=1\).

Step2: Analyze line properties

Parallel lines have equal slopes and never intersect. Perpendicular lines have slopes that multiply to \(-1\) (here \(m_1\times m_2 = 1\times1 = 1
eq -1\), so not perpendicular). Since both slopes are equal, the lines are parallel and never intersect.

Step3: Evaluate options

• Option 1: Wrong (perpendicular definition is wrong, and slopes show parallel).
• Option 2: Wrong (parallel lines don’t intersect at \(90^\circ\)).
• Option 3: Wrong (slopes aren’t negative reciprocals, so not perpendicular).
• Option 4: Correct (equal slopes mean parallel, and parallel lines never intersect).

Answer:

D. The lines are parallel because they will never touch or intersect.