Final answer:
To find the linear function f which passes through (-3, 1) and (13, 5), calculate the slope and y-intercept. The slope is 1/4, and using y = mx + b with one point gives the y-intercept as 7/4. Hence, f(x) = (1/4)x + 7/4.
Step-by-step explanation:
To write a linear function f with the given conditions f(-3) = 1 and f(13) = 5, we first need to find the slope of the line, which is the change in the y-value divided by the change in the x-value.
Using the formula for slope m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the given points, we have:
m = (5 - 1) / (13 - (-3))
= 4 / 16
= 1/4
With the slope of 1/4, we can now use one of the given points to find the y-intercept (b).
Let's use the point (-3, 1) with the slope-intercept form of a linear equation, y = mx + b, where m is the slope and b is the y-intercept:
- y = (1/4)x + b
- 1 = (1/4)(-3) + b
- 1 = -3/4 + b
- 1 + 3/4 = b
- b = 7/4
The linear function f is then f(x) = (1/4)x + 7/4.