Question

Slope intercept form

Answer 1

Given:

The equation of the parallel line is

$y=-\dfrac{5}{2}x+7$

The required line passes through the point (-4,1).

To find:

The equation of line in slope slope intercept form.

Solution:

The slope intercept form of a linear function is

$y=mx+b$

Where m is slope and b is y-intercept.

On comparing the equation $y=-\dfrac{5}{2}x+7$ with slope intercept form, we get

$m=-\dfrac{5}{2}$

We know that the slopes of parallel lines are always same. So, the slope of the required line is $m=-\dfrac{5}{2}$.

The line passes through the point (-4,1) with slope $m=-\dfrac{5}{2}$. So, the equation of line is

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

$y-(1)=-\dfrac{5}{2}(x-(-4))$

$y-1=-\dfrac{5}{2}(x+4)$

$y-1=-\dfrac{5}{2}x-10$

Adding 1 on both sides, we get

$y=-\dfrac{5}{2}x-10+1$

$y=-\dfrac{5}{2}x-9$

Therefore, the correct option is C.