Final answer:
The student's question involves calculating the slope of a line between two points and then using one of the points to determine the y-intercept for the equation of the line in slope-intercept form, y = mx + b.
Step-by-step explanation:
The student's question is related to the slope and the y-intercept of a linear equation in slope-intercept form. Since the question provides two points that lie on the line, we can find the slope (m) by using the formula for the slope between two points, which is (y2 - y1) / (x2 - x1). Once we have the slope, we can use one of the points and the slope to write the equation of the line in slope-intercept form, which is y = mx + b, where b is the y-intercept.
First, let's calculate the slope using the provided points (-7x,6) and (4,-7):
- m = (y2 - y1) / (x2 - x1) = (-7 - 6) / (4 - (-7x))
- m = -13 / (4 + 7x)
Now, choose one of the points, say (-7x,6), and plug it into the slope-intercept form equation along with the calculated slope:
- 6 = (-13 / (4 + 7x))(-7x) + b
- Solve for b to find the y-intercept.
Once we have the value of b, we can write the final equation of the line:
- y = (-13 / (4 + 7x))x + b