Final answer:
To find the equation of a line that passes through (7, -4) and (-1, 2), we calculate the slope as -3/4 and then determine the y-intercept as 5/4, resulting in the line's equation in slope-intercept form: y = -3/4x + 5/4.
Step-by-step explanation:
The equation of the line that passes through the points (7, -4) and (-1, 2) can be written in slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept. To find the slope, we use the formula m = (y2 - y1) / (x2 - x1).
First, calculate the slope:
m = (2 - (-4)) / (-1 - 7) = 6 / (-8) = -3/4
Now, use one of the points and the slope to find the y-intercept (b) by plugging into the slope-intercept form:
-4 = (-3/4)(7) + b
b = -4 + (3/4)(7)
b = -4 + 21/4 = -16/4 + 21/4
b = 5/4
Therefore, the equation of the line in slope-intercept form is:
y = -3/4x + 5/4