Question

Write a linear function f with f(-3) = 1 and f(13) = 5

Answer 1

To find the linear function, we need to first determine the slope (m) and y-intercept (b) from the given information.

Given:
f(-3) = 1
f(13) = 5

Using the slope-intercept form of a linear equation (y = mx + b) and substituting the coordinates for the points (-3,1) and (13,5), we can form linear equations as follows:

1 = -3m + b
5 = 13m + b

Now, let's solve the above system of equations to find the values of m and b.

Subtracting the first equation from the second equation:
5 - 1 = 13m + b - (-3m + b)
4 = 13m + 3m
4 = 16m

Dividing both sides by 16:
4/16 = m
1/4 = m

Now, substitute this value of m into the first equation to solve for b:
1 = -3(1/4) + b
1 = -3/4 + b
1 + 3/4 = b
4/4 + 3/4 = b
7/4 = b

Therefore, the linear function f(x) is:
f(x) = (1/4)x + 7/4