Final answer:
The slope-intercept form of the line through (3,-4) and (5,4) is y = 4x - 16.
Step-by-step explanation:
To find the slope intercept form of a line, we use the formula:
y = mx + b
where m represents the slope and b represents the y-intercept. Given the points (3, -4) and (5, 4), we can find the slope by using the formula:
m = (y2 - y1) / (x2 - x1)
Substituting the coordinates, we get:
m = (4 - (-4)) / (5 - 3)
m = 8 / 2
m = 4
Now, we can substitute one of the points and the slope into the formula to find the y-intercept:
-4 = 4(3) + b
b = -4 - 12
b = -16
Therefore, the slope-intercept form of the line passing through (3, -4) and (5, 4) is y = 4x - 16.