Question

Two lines are graphed on a coordinate plane. The equation of the first line is 2x - y = 6 and the equation of the second line is x + 2y = 10. Describe the relationship between the two lines and how you know. Do the equations represent parallel lines, perpendicular lines, coinciding lines (i.e., the same line), or intersecting lines that are not perpendicular? If the lines intersect, identify the point of intersection.
*
1 point
Coinciding Lines
Intersecting Lines at (2.8, 4.4)
Intersecting Lines at (4.4, 2.8)
Parallel Lines
Perpendicular Lines

Answer 1

Rewrite each in slope-intercept form: 2x - y = 6 → y = 2x - 6 (slope 2).
x + 2y = 10 → y = -1/2 x + 5 (slope -1/2).

The slopes are negative reciprocals (2 · -1/2 = -1), so the lines are perpendicular. Solving the system gives the intersection: x + 2(2x - 6) = 10 → 5x = 22 → x = 22/5 = 4.4; y = 2x - 6 = 14/5 = 2.8.

Answer: Perpendicular lines; they intersect at (4.4, 2.8).