Final answer:
The equation in slope-intercept form for the line passing through the points (7, 2) and (2, 12) is y = -2x + 16.
Step-by-step explanation:
To write an equation in slope-intercept form for the line that passes through the points (7, 2) and (2, 12), you first need to find the slope (m) of the line. The slope is calculated using the formula m = (Y2 - Y1) / (X2 - X1), where (X1, Y1) and (X2, Y2) are the given points. In this case, the slope m is calculated as follows:
m = (12 - 2) / (2 - 7) = 10 / (-5) = -2
The slope of the line is -2. Next, we use one of the points to find the y-intercept (b) by substituting the slope and the point into the slope-intercept equation y = mx + b. Let's use the point (7, 2).
2 = (-2) × 7 + b
b = 2 - ((-2) × 7)
b = 2 + 14
b = 16
The y-intercept b is 16. Hence, the equation of the line in slope-intercept form is:
y = -2x + 16