To write the equation of a line in slope-intercept form, which is y = mx + b, we first need to find the slope (m) and the y-intercept (b).
The slope (m) of the line is found by calculating the change in y divided by the change in x (rise over run) between two points on the line. Using the points (-7, 1) and (-4, -8):
Slope (m) = (y2 - y1) / (x2 - x1)
= (-8 - 1) / (-4 - (-7))
= (-8 - 1) / (-4 + 7)
= (-9) / (3)
= -3
Now that we have the slope, we can use it along with one of the points to find the y-intercept (b). Let's use the point (-7, 1):
y = mx + b
1 = (-3)(-7) + b
1 = 21 + b
b = 1 - 21
b = -20
So, the y-intercept is -20.
Now we can write the equation of the line in slope-intercept form:
y = mx + b
y = -3x - 20
So the equation of the line that passes through the points (-7, 1) and (-4, -8) in slope-intercept form is y = -3x - 20.
