Final answer:
Brooke's error was in using invalid sums to find the y-intercept. The correct y-intercept is found by using the slope, which is -4, derived from the given points, and by substituting into y = mx + b using one of the points, resulting in y = -4x - 3.
Step-by-step explanation:
The error in Brooke's method of finding the equation of the line in slope-intercept form is that she incorrectly used values for finding the y-intercept (b) that are not connected to the given points (-7, 25) and (-4, 13). To find the slope (m), we need to use the formula m = (y2 - y1) / (x2 - x1) using the coordinates of the two given points. To find the y-intercept, we can use one of the points and the slope in the slope-intercept equation, y = mx + b, and solve for b.
To calculate the slope:
m = (13 - 25) / (-4 - (-7))
= -12 / 3
= -4
Therefore, the slope (m) is -4. Now, using one of the points, say (-7, 25), we substitute the values into the equation y = mx + b:
25 = -4(-7) + b
= 28 + b
= b - 28.
To find b, subtract 28 from both sides:
b = 25 - 28
= -3.
The equation of the line, in slope-intercept form, is y = -4x - 3.