Explanation:
The slope-intercept form of the equation of a line that passes through (5, -4) and has a slope of 3/4 is y = (3/4)x - 31/4.
What is the slope-intercept form?
The slope-intercept form of a line is y=mx + c.
Where, x and y are coordinates. m = slope and c = y intercept.
Given, slope (m) = 3/4
Substituting the values of (x, y) as (5, -4) and m = 3/4, we get:
-4 = (3/4) × 5 + c
⇒ c = -4 - (3/4) × 5 = -4 - 15/4 = -31/4
Now, putting the value of c in the standard equation:
y = (3/4)x - 31/4
⇒ 4y = 3x - 31
⇒ 3x - 4y = 31
Answer is Option C