Determine whether the graphs of the pair of equations are parallel, perpendicular, or neither. $7 x + 6 y = 9,6 x - 7 y = 6$
A) perpendicular
B) parallel
C) neither

Question

Quizplus · Accepted Answer

We can rewrite both equations in slope-intercept form (y=mx+b) by solving for y:
$$7x+6y=9 \implies 6y=-7x+9 \implies y= -\frac{7}{6}x+\frac{3}{2}$$
$$6x-7y=6 \implies -7y = -6x+6 \implies y=\frac{6}{7}x-\frac{6}{7}$$
The slope of the first equation is $-\frac{7}{6}$ and the slope of the second equation is $\frac{6}{7}$. We can see that these slopes are negative reciprocals of each other: $$-\frac{7}{6}\cdot\frac{6}{7}=-1$$
Therefore, the graphs of the two equations are perpendicular.

Determine Whether the Graphs of the Pair of Equations Are 7x+6y=9,6x−7y=67 x + 6 y = 9,6 x - 7 y = 67x+6y=9,6x−7y=6

Determine Whether the Graphs of the Pair of Equations Are $7 x + 6 y = 9,6 x - 7 y = 6$