Question

Maria and Nate graphed lines on a coordinate plane. Maria's line is represented by the equation y = -5/6x +8. Nate's line is perpendicular to Maria's line. Which of the following could be an equation for Nate's line?
a 5x-6y=15
b 5x+6y=15
c 6x-5y=15
d 6x+5y=15

Answer 1

Answer:

c)   6x - 5y = 15

Step-by-step explanation:

Slope-intercept form of a linear equation:  $y=mx+b$

(where m is the slope and b is the y-intercept)

Maria's line:  $y=-\dfrac{5}{6}x+8$

Therefore, the slope of Maria's line is $-\frac{5}{6}$

If two lines are perpendicular to each other, the product of their slopes will be -1.

Therefore, the slope of Nate's line (m) is:

$\begin{aligned}\implies m \times -\dfrac{5}{6} &=-1\\m & =\dfrac{6}{5}\end{aligned}$

Therefore, the linear equation of Nate's line is:

$y=\dfrac{6}{5}x+b\quad\textsf{(where b is some constant)}$

Rearranging this to standard form:

$\implies y=\dfrac{6}{5}x+b$

$\implies 5y=6x+5b$

$\implies 6x-5y=-5b$

Therefore, option c could be an equation for Nate's line.