Question

If the graphs of the linear equations shown below are perpendicular, what is the value
of a?
y = 3x +8
2y = ax - 5

Answer 1

Answer:

$a=-\frac{2}{3}$

Step-by-step explanation:

We are given the lines, $y=3x+8$ and $2y=ax-5$. For the latter equation, we can isolate the variable y to have the same format as the first. We want to create a y=mx+b equation where m represents the slope of the line. We now have the equations:

$y=3x+8$ and

$y=\frac{a}{2}x-2.5$

The definition of perpendicular lines is that their slopes must be the negative reciprocal of each other. Thus:

$-\frac{1}{3}=\frac{a}{2} \\\\a=-\frac{2}{3}$

I hope this helps! Let me know if you have any questions :)