For the following pair of equations, predict whether they represent parallel lines, perpendicular lines, or lines that intersect but are not perpendicular. 4.9 x + 2.1 y = 5.4 and 2.1 x - 4.9 y = 8.7
A) parallel lines
B) lines that intersect but are not perpendicular
C) perpendicular lines

Question

Quizplus · Accepted Answer

To determine the relationship between the two lines, we can compare their slopes. The slope-intercept form of a line is y = mx + b, where m is the slope. For the first equation, 4.9x + 2.1y = 5.4, we can solve for y to find the slope: 2.1y = -4.9x + 5.4, y = (-4.9/2.1)x + (5.4/2.1). For the second equation, 2.1x - 4.9y = 8.7, solving for y gives: -4.9y = -2.1x + 8.7, y = (2.1/4.9)x - (8.7/4.9). The slopes are -4.9/2.1 and 2.1/4.9, which are negative reciprocals of each other. This means the lines are perpendicular.

For the Following Pair of Equations, Predict Whether They Represent