Final answer:
To write the equation of the line, we can use the point-slope form of a line and the given point (8, -3) and slope of 5/4. The equation in slope-intercept form is y = (5/4)x - 13.
Step-by-step explanation:
To write the equation of a line in slope-intercept form, we need the slope and a point on the line. Given that the line passes through the point (8, -3) and has a slope of 5/4, we can use the point-slope form of a line to write the equation. The point-slope form is y - y1 = m(x - x1), where (x1, y1) is the point on the line and m is the slope. Plugging in the values, we have y - (-3) = (5/4)(x - 8). Simplifying this gives us the equation y + 3 = (5/4)(x - 8).
To convert this equation to slope-intercept form, we need to isolate y. Distribute the slope: y + 3 = (5/4)x - 10. Then, subtract 3 from both sides: y = (5/4)x - 13. Finally, rearrange the terms to have the slope-intercept form y = mx + b, where m is the slope and b is the y-intercept. The equation in slope-intercept form for the given line is y = (5/4)x - 13.