Question

Find the equation of a line which intersects $y=\frac{x}{3}+5$ at $(9,8)$ and does not intersect the line $y=-3x-7$.

• A. $y=-3x+13$
• B. $y=-3x+35$
• C. $y=-\frac{x}{3}+8$
• D. $y=-\frac{x}{3}+11$
• E. $y=\frac{x}{3}-7$

Answer 1

The correct option is B $y=-3x+35$

Given equation of line is

$y=\frac{x}{3}+5$ then slope of line is $\frac{1}{3}$

And second equation $y=-3x-7$ the slope of line is $-3$.

Two lines are parallel if and only if they have exactly the same slope.

Then line passes through point $(9,8)$ and slope is $-3$ is

$(y-8)=-3(x-9)$

$\Rightarrow y-8=-3x+27$

$\Rightarrow y=-3x+27+8$

$\Rightarrow y=-3x+35$