Question

6. Find the equation in slope-intercept form for the line that passes through the point (-8, 3) and is parallel

Answer 1

The equation in slope-intercept form for the line that passes through the point (-8, 3) and is parallel  to the line -5x + 4y = 8 is:

$y = \frac{5}{4}x + 13$

Solution:

Given that,

We have to find the equation in slope-intercept form for the line that passes through the point (-8, 3) and is parallel  to the line -5x + 4y = 8

The equation of line in slope intercept form is given as:

y = mx + c

Where "m" is the slope of line

From given,

-5x + 4y = 8

Rearrange to slope intercept form

4y = 5x + 8

$y = \frac{5x}{4} + \frac{8}{4}\\\\y = \frac{5x}{4} + 2$

On comparing the above equation with slope intercept form,

$m = \frac{5}{4}$

We know that, slopes of parallel lines are equal

Therefore, slope of line parallel  to the line -5x + 4y = 8 is:

$m = \frac{5}{4}$

$\text{Substitute } m = \frac{5}{4}\ and\ (x, y) = (-8, 3) \text{ in eqn 1}$

$3 = \frac{5}{4} \times -8 + c\\\\3 = -10 + c\\\\c = 13$

Substitute c = 13 and m = 5/4 in eqn 1

$y = \frac{5}{4}x + 13$

Thus the equation of line in slope intercept form is found