Final answer:
To find the slope-intercept form, we need to find the slope and the y-intercept of the line. The slope can be found using the formula (y2-y1)/(x2-x1), and then we can substitute the slope and any point into the equation to solve for the y-intercept.
Step-by-step explanation:
The slope-intercept form of a linear equation is y = mx + b, where m is the slope and b is the y-intercept.
To find the slope, we apply the formula:
m = (y2-y1)/(x2-x1)
Using the points (2,-3) and (-1/2, 1/8), the slope can be calculated as:
m = (1/8 - (-3))/(-1/2 - 2) = (1/8 + 3)/(-5/2) = 25/8
Now, substitute the slope and any one of the given points into the equation and solve for b.
Using the point (2,-3):
-3 = (25/8)(2) + b
Solving for b:
b = -3 - (25/4) = -3 - 6.25 = -9.25
Therefore, the slope-intercept form of the line passing through the points (2,-3) and (-1/2, 1/8) is y = (25/8)x - 9.25.