c) 6x - 5y = 15
Step-by-step explanation:
Slope-intercept form of a linear equation: [tex]y=mx+b[/tex]
(where m is the slope and b is the y-intercept)
Maria's line: [tex]y=-\dfrac{5}{6}x+8[/tex]
Therefore, the slope of Maria's line is [tex]-\frac{5}{6}[/tex]
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:
[tex]\begin{aligned}\implies m \times -\dfrac{5}{6} &=-1\\m & =\dfrac{6}{5}\end{aligned}[/tex]
Therefore, the linear equation of Nate's line is:
[tex]y=\dfrac{6}{5}x+b\quad\textsf{(where b is some constant)}[/tex]
Rearranging this to standard form:
[tex]\implies y=\dfrac{6}{5}x+b[/tex]
[tex]\implies 5y=6x+5b[/tex]
[tex]\implies 6x-5y=-5b[/tex]
Therefore, option c could be an equation for Nate's line.