What is the slope-intercept form of the equation of a line that passes through (5, -4) and has a slope of `3/4`? a. `y = -(3)/(4) x -(1)/(4)` b. `y = 3/4 x +(1)/(4)` c. `y = 3/4 x -(31)/(4)` d. `y = 3/4 x +(31)/(4)`

Your answer would be C. y = (3/4)x - 31/4

We can find this first by using the slope we are given to write the equation y = (3/4)x + c. Then, we can substitute in the coordinates and solve:

-4 = (3/4 × 5) + c

-4 = 15/4 + c

- 15/4

-4 - 15/4 = c

To do this subtraction, we must first write -4 as -4/1, and then get it over 4 by multiplying by 4, so we get the fraction -16/4.

Then we can do -16/4 - 15/4 = -31/4, which is your y-intercept.

This makes the final answer y = (3/4)x - 31/4.

I hope this helps!

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step-by-step explanation: