A line passes through the points (4,
–
1) and (7,14). Write its equation in slope-intercept form.
Write your answer using integers, proper fractions, and improper fractions in simplest form.
First, let's find the slope of the line using the formula:
slope = (y2 - y1) / (x2 - x1)
Using the points (4, -1) and (7,14):
slope = (14 - (-1)) / (7 - 4)
slope = (15) / (3)
slope = 5
Now that we have the slope, we can use one of the points to find the y-intercept:
Using the point (4, -1) and the slope of 5:
y = mx + b
-1 = 5(4) + b
-1 = 20 + b
b = -21
The equation of the line in slope-intercept form is:
y = 5x - 21