Question

Find the equation of a line which passes through the point $(6,-5)$ and has an intercept of $3$ with the $x$-axis.

• A. $y=-\frac{5}{3}x+5$
• B. $y=-\frac{4}{3}x+3$
• C. $y=-\frac{3}{5}x+3$
• D. $y=\frac{5}{3}x+5$

Answer 1

Answer: (A)

$y=-\frac{5}{3}x+5$

In given question a line passes through the point $(6,-5)$ and has an intercept of $3$ with the $x$-axis

Then second point is line passes is $(3,0)$

Then the line passes through point $(6,-5)$ and $(3,0)$.

Slope of line $=$ $\frac{0-(-5)}{3-6}=\frac{5}{-3}=-\frac{5}{3}$

Then the line passes through slope $-\frac{5}{3}$ and point $(3,0)$ is

$y-0=-\frac{5}{3}(x-3)\Rightarrow 3y=-\frac{5}{3}x+5$