Final answer:
The equation of the line in slope-intercept form that goes through points (7, 2) and (5, 10) is y = -4x + 30. This is determined by first finding the slope, m, which is -4, and then using one of the points to solve for the y-intercept, b, which is 30.
Step-by-step explanation:
To write the equation of a line in slope-intercept form that goes through the points (7, 2) and (5, 10), we need to find the slope (m) and the y-intercept (b) of the line.
First, let's calculate the slope using the two given points. The slope formula is m = (y2 - y1) / (x2 - x1). Substituting the points into the formula:
m = (10 - 2) / (5 - 7) = 8 / (-2) = -4
Now that we have the slope, we can use one of the points to find the y-intercept. Let's use point (7, 2) and the slope-intercept equation y = mx + b. Substituting in the values gives us:
2 = (-4)(7) + b
Solving for b, we get:
b = 2 + 28 = 30
Therefore, the equation of the line in slope-intercept form is y = -4x + 30.