Final answer:
The slope-intercept form of the equation of a line that passes through (5,-4) with a slope of 3/4 is y = 3/4 x - 31/4. By substituting the point and slope into the slope-intercept equation and solving for the y-intercept, we can find the correct equation, which is option c.
Step-by-step explanation:
The question asks for the slope-intercept form of the equation of a line that passes through the point (5,-4) and has a slope of 3/4. The slope-intercept form is given by y = mx + b, where m is the slope and b is the y-intercept. To find the y-intercept, we use the point given and the slope to solve for b in the equation.
We start by plugging the given point and slope into the slope-intercept equation: -4 = (3/4)(5) + b. Simplify to find the value of b: -4 = 15/4 + b, which yields b = -31/4. Therefore, the slope-intercept form of the line is y = 3/4 x - 31/4, which matches option c.