Question

Find the equation of a line that passes through (-5,4) and us parallel to y=-6/7x+3​

Answer 1

Given:

The given equation of line is

$y=-\dfrac{6}{7}x+3$

To find:

The equation of line that passes through (-5,4) and is parallel to the given line.

Solution:

Slope intercept form of a line is

$y=mx+b$    ...(i)

where, m is slope and b is y-intercept.

We have,

$y=-\dfrac{6}{7}x+3$      ...(ii)

On comparing (i) and (ii), we get

$m=-\dfrac{6}{7}$

Slope of given line is $m=-\dfrac{6}{7}$.

Slope of parallel lines are same. So, slope of parallel line is $m=-\dfrac{6}{7}$.

The required line passes through (-5,4) with slope $m=-\dfrac{6}{7}$. So, the equation of line is

$y-y_1=m(x-x_1)$

$y-4=-\dfrac{6}{7}(x-(-5))$

$y-4=-\dfrac{6}{7}(x+5)$

$y-4=-\dfrac{6}{7}x-\dfrac{30}{7}$

Adding 4 on both sides, we get

$y=-\dfrac{6}{7}x-\dfrac{30}{7}+4$

$y=-\dfrac{6}{7}x+\dfrac{-30+28}{7}$

$y=-\dfrac{6}{7}x-\dfrac{2}{7}$

Therefore, the correct option is a.