To find the equation of the line that passes through the points (7, 2) and (2, 12) in slope-intercept form (y = mx + b), you first need to calculate the slope (m) and then use one of the points to solve for the y-intercept (b).
Calculate the slope (m):
Use the formula for slope, which is (y2 - y1) / (x2 - x1), where (x1, y1) = (7, 2) and (x2, y2) = (2, 12).
m = (12 - 2) / (2 - 7)
m = 10 / (-5)
m = -2
Now that you have the slope (m), you can use one of the points (let's use (7, 2)) to find the y-intercept (b).
2 = (-2)(7) + b
Now, solve for b:
2 = -14 + b
Add 14 to both sides:
b = 2 + 14
b = 16
Now, you have the slope (m) and the y-intercept (b). Combine them to write the equation in slope-intercept form:
y = mx + b
y = -2x + 16
So, the equation of the line passing through (7, 2) and (2, 12) in slope-intercept form is:
y = -2x + 16