[tex]y = \frac{5}{4}x + 13[/tex]
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
[tex]y = \frac{5x}{4} + \frac{8}{4}\\\\y = \frac{5x}{4} + 2[/tex]
On comparing the above equation with slope intercept form,
[tex]m = \frac{5}{4}[/tex]
We know that, slopes of parallel lines are equal
Therefore, slope of line parallel to the line -5x + 4y = 8 is:
[tex]m = \frac{5}{4}[/tex]
[tex]\text{Substitute } m = \frac{5}{4}\ and\ (x, y) = (-8, 3) \text{ in eqn 1}[/tex]
[tex]3 = \frac{5}{4} \times -8 + c\\\\3 = -10 + c\\\\c = 13[/tex]
Substitute c = 13 and m = 5/4 in eqn 1
[tex]y = \frac{5}{4}x + 13[/tex]
Thus the equation of line in slope intercept form is found
