Final answer:
The equation of the secant line joining the points (-5, -12) and (7, 0) is y = x - 7.
Step-by-step explanation:
The question involves finding the equation of a secant line that joins two given points on the graph of the function f(x) = x² − x − 42. To do this, we must calculate the slope of the secant line using the formula slope = (y2 - y1) / (x2 - x1). Once we have the slope, we can use the point-slope form of the line equation, y - y1 = slope × (x - x1), to find the equation of the secant line.
For the points (-5, -12) and (7, 0), the slope of the secant line is calculated as follows:
- slope = (0 - (-12)) / (7 - (-5)) = 12 / 12 = 1.
With the slope of 1 and using one of the points, let's use (-5, -12), we can form the equation:
- y - (-12) = 1 × (x - (-5))
- y + 12 = x + 5
- y = x - 7
Thus, the equation of the secant line is y = x - 7.