# Slope of a Line Between Two Points on a Function Exercises

### Example 1

For the given function *f* and values of *a* and *b*, find the slope of the secant line between the points (*a*, *f*(*a*)) and (*b*, *f*(*b*)):

*f*(*x*) = *x*^{2}, *a* = 1, *b* = 2.

### Example 2

For the given function *f* and values of *a* and *b*, find the slope of the secant line between the points (*a, f*(*a*)) and (*b*, *f*(*b*)):

*f*(*x*) = *x*^{2}, *a* = 1, *b* = 1.5.

### Example 3

For the given function *f* and values of *a* and *b*, find the slope of the secant line between the points (*a, f*(*a*)) and (*b*, *f*(*b*)):

*f*(*x*) = sin(*x*), *a* = 0, *b* = π/2.

### Example 4

For the given function *f* and values of *a* and *b*, find the slope of the secant line between the points (*a, f*(*a*)) and (*b*, *f*(*b*)):

*f*(*x*) = *x*^{3} – 2*x* + 3, *a* = 1, *b* = 4.

### Example 5

For the given function *f* and values of *a* and *b*, what is the slope of the secant line between the points (*a, f*(*a*)) and (*b*, *f*(*b*))?

*f*(*x*) = *x*^{4 }– 2, *a* = -2, *b* = 2.

### Example 6

Given the values of *a* and *b*, what must *h* be so that *a* + *h* = *b*?

*a* = 4, *b* = 4.25.

### Example 7

Given the values of *a* and *b*, what must *h* be so that *a* + *h* = *b*?

*a* = -1, *b* = -1.5.

### Example 8

For the given function *f*, value of *a*, and value of *h*, what is the slope of the secant line between (*a*, *f*(*a*)) and (*a* + *h*, *f*(*a* + *h*))?

*f*(*x*) = *x*^{2}, *a* = 1, *h* = 0.1.

### Example 9

For the given function *f*, value of *a*, and value of *h*, what's the slope of the secant line between (*a*, *f*(*a*)) and (*a* + *h*, *f*(*a* + *h*))?

*f*(*x*) = 1 – *x*^{2}, *a* = 0, *h* = 0.1.

### Example 10

For the given function *f*, value of *a*, and value of *h*, what's the slope of the secant line between (*a*, *f*(*a*)) and (*a* + *h*, *f*(*a* + *h*))?

*f*(*x*) = cos(*x*), *a* = 0, *h* = -π/2.

### Example 11

For the given function *f*, value of *a*, and value of *h*, what's the slope of the secant line between (*a*, *f*(*a*)) and (*a* + *h*, *f*(*a* + *h*))?

*f*(*x*) = *x*^{3}– *x*, *a* = 1, *h* = 4.

### Example 12

*f*, value of *a*, and value of *h*, what's the slope of the secant line between (*a*, *f*(*a*)) and (*a *+ *h*, *f*(*a* + *h*))?

*f*(*x*) = 3*x*, *a* =* -*2,and* h* = -0.2.