Final answer:
The slope-intercept form of the equation of a line is y = mx + b, where m represents the slope and b represents the y-intercept. Given that the line passes through the point (5,-4) and has a slope of 3/4, the correct equation is y = (3/4)x + (31/4).
Step-by-step explanation:
The slope-intercept form of the equation of a line is given by y = mx + b, where m represents the slope and b represents the y-intercept.
Given that the line passes through the point (5,-4) and has a slope of 3/4, we can substitute these values into the equation to find the correct form. Plugging in the values for m and b, we get: y = (3/4)x + b
To find the value of b, we substitute the coordinates of the point (5,-4) into the equation: -4 = (3/4)(5) + b
Simplifying this equation, we get: -4 = 15/4 + b
Moving the constant term to the other side, we have: -4 - 15/4 = b
Combining like terms, we get: -16/4 - 15/4 = b
Simplifying further, we have: -31/4 = b
Now we can substitute the value of b back into the equation: y = (3/4)x - 31/4
Therefore, the correct answer is D. y = (3/4) x + (31/4).