Question

A line has a slope of $\frac{3}{4}$ and passes through the point $(-12,-39)$. At which point does this line intersect the x-axis?

• A. $(40,0)$
• B. $(10,0)$
• C. $(-40,0)$
• D. $(20,0)$

Answer 1

The correct option is A $(40,0)$

Let the equation of the line is $y=mx+c$

The slope of the line is given $m=\frac{3}{4}$

Also the line passes through the point $(-12,-39)$

Putting the point in the equation of line, we get,

$\Rightarrow -39=\frac{3}{4}(-12)+c$

$\Rightarrow c=-30$

Hence the equation of the line becomes $y=\frac{3}{4}x-30$

The line intersects the $x$ axis where the $y$ coordinate is zero.

Putting $y=0$ in equation of the line, we get, $x=40$

Hence the line cuts the $x$ axis at $(40,0)$

Correct option is $A$.