Explanation:
Use the function to find the coordinates of the endpoints. Find the slope between those points, then use point-slope form to write the equation. If you wish, you can simplify to slope-intercept form.
For example, #66:
f(2) = -4(2) + 1 = -7
f(5) = -4(5) + 1 = -19
So the endpoints of the secant line are (2, -7) and (5, -19). The slope between those lines is:
m = (-19 − (-7)) / (5 − 2)
m = -12 / 3
m = -4
The equation of the line in point-slope form is:
y − (-7) = -4 (x − 2)
y + 7 = -4 (x − 2)
Simplifying:
y + 7 = -4x + 8
y = -4x + 1
f(x) is a line, so unsurprisingly, the secant line connecting two points on that line has the same equation.
Let's try #68:
g(2) = (-1)² + 1 = 2
g(5) = (2)² + 1 = 5
So the endpoints of the secant line are (-1, 2) and (2, 5). The slope between those lines is:
m = (5 − 2) / (2 − (-1))
m = 3 / 3
m = 1
The equation of the line in point-slope form is:
y − 2 = 1 (x − (-1))
y − 2 = x + 1
Simplifying:
y = x + 3