Question

The number of lines that are parallel to $2x+6y-7=0$ and have an intercept $10$ units between the coordinate axes is

• A. $1$
• B. $2$
• C. $4$
• D. Infinitely many

Answer 1

Answer: (B)

$2$

The slope of the given line is $m=\frac{-1}{3}$

Therefore, the slope of any line parallel to the given line is also $m=\frac{-1}{3}$

The slope intercept form of any parallel line is $y=\frac{-1}{3}x+c$ where $c$ is the y-intercept.

Thus, the x-intercept is $(3c,0)$ and the y-intercept is $(0,c).$

The distance between the intercepts is to be $10units$, therefore, using the distance formula

$10=\sqrt{(3c{)}^2+c^2}$

$100=9c^2+c^2$

$c=\pm \sqrt{10}$

There are two lines parallel to the given line, such that the distance between the x and y intercepts is 10 units , their equations are:

$y=\frac{-1}{3}x+\sqrt{10}$

And

$y=\frac{-1}{3}x-\sqrt{10}$