Final answer:
To find the equation of a line in slope-intercept form given a point and slope, substitute the slope and the coordinates of the point into the formula y = mx + b to solve for the y-intercept, b. The final equation for the line passing through (-8,-1) with a slope of 5/4 is y = (5/4)x + 9.
Step-by-step explanation:
The subject of the question involves finding the equation of a straight line in slope-intercept form when given a point and the slope of the line. The slope-intercept form of a line is y = mx + b, where m is the slope, and b is the y-intercept. In this case, the slope (m) is given as 5/4, and the line passes through the point (-8,-1).
Firstly, we plug the known slope and point values into the slope-intercept equation to solve for b (the y-intercept):
y = mx + b-1 = (5/4)(-8) + b
This simplifies to:
-1 = -10 + b
Adding 10 to both sides, we find:
b = 9
With the y-intercept determined, the final equation of the line is:
y = (5/4)x + 9
This equation means that for every increase of 1 on the horizontal axis, there is a rise of 5/4 on the vertical axis, and the line intersects the y-axis at 9.