Question

The lines given by the equations 3y + 2x = 7 and y = mx − 11 are perpendicular. Find m

Answer 1

Answer:

$m=\frac{3}{2}$

Step-by-step explanation:

When two lines are perpendicular, their slopes will be opposite reciprocals:

$-3$ → $\frac{1}{3}$

$\frac{1}{4}$ → $-4$

Solve the first equation for y to rewrite in slope-intercept form:

$y=mx+b\\\\3y+2x=7\\\\3y+2x-2x=7-2x\\\\3y=-2x+7\\\\\frac{3y}{3}=\frac{-2x}{3} +\frac{7}{3} \\\\y=-\frac{2}{3}x+\frac{7}{3}$

m is the slope, so the slope of this line is $-\frac{2}{3}$. The opposite reciprocal is $\frac{3}{2}$, therefore, m is $\frac{3}{2}$