Final answer:
The equation of the line through (7, -4) and (-1, 3) has a slope of -7/8. It can be written in a point-slope form as y + 4 = -7/8(x - 7), and in slope-intercept form as y = -7/8x + 25/8.
Step-by-step explanation:
To write the equation of the line that passes through the points (7, –4) and (–1, 3), the first step is to find the slope of the line. The slope (m) is given by the rise over run, which is the change in y divided by the change in x:
m = (3 - (-4)) / (-1 - 7) = 7 / -8 = -7/8
Now that we have the slope, we can use the point-slope form which is given by the formula:
y - y1 = m(x - x1)
We can choose one of the points for x1 and y1; let's use (7, -4):
y - (-4) = -7/8(x - 7)
Therefore, the point-slope form of the line is:
y + 4 = -7/8(x - 7)
Now, to convert this into the slope-intercept form (y = mx + b), we just solve for y:
y = -7/8x + 7/8 × 7 - 4
After simplifying the constant term:
y = -7/8x + 25/8
The slope-intercept form is y = -7/8x + 25/8, where -7/8 is the slope and 25/8 is the y-intercept.