Final answer:
To find the slope-intercept form of the line through (3/8, 0) and (5/8, 1/2), first calculate the slope, which is 2, and then use one of the points to solve for the y-intercept, which is -3/4. The final equation is y = 2x - 3/4.
Step-by-step explanation:
To find the slope-intercept form of the line passing through the points (3/8, 0) and (5/8, 1/2), first calculate the slope (m) of the line. The slope is defined as the rise over the run, which means we take the change in the y-values divided by the change in the x-values between the two points.
m = (y2 - y1) / (x2 - x1)
m = (1/2 - 0) / (5/8 - 3/8)
m = (1/2) / (2/8)
m = (1/2) / (1/4)
m = 2
Now that we have the slope, we can use one of the points to find the y-intercept (b). The slope-intercept form of a line is given by y = mx + b. Let's use the point (3/8, 0) and the slope we just found.
0 = 2*(3/8) + b
0 = 3/4 + b
b = -3/4
Therefore, the slope-intercept form of the line is y = 2x - 3/4.