Final answer:
To write the equation of the line that passes through two given points in slope-intercept form, find the slope using the formula (y2 - y1) / (x2 - x1), and then find the y-intercept by substituting one of the points into the equation y = mx + b.
Step-by-step explanation:
To write the equation of the line that passes through two given points in slope-intercept form, we need to find the slope and the y-intercept of the line.
The slope, m, can be found using the formula: m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the coordinates of the two given points.
Using the points (7, 2) and (2, 12), the slope is:
m = (2 - 12) / (7 - 2) = -2
To find the y-intercept, we can substitute the slope and one of the points into the equation y = mx + b and solve for b. Using the point (7, 2):
2 = -2 * 7 + b
b = 16
Therefore, the equation of the line in slope-intercept form is: y = -2x + 16.