Final answer:
To find a linear function with a slope of ⅓ that passes through the point (-15, -13), we use the slope-intercept form to calculate the y-intercept b, which results in the linear function f(x) = ⅓x - 4.
Step-by-step explanation:
To find a linear function f(x) with a given slope and a point, we can use the slope-intercept form of a linear equation: y = mx + b, where m is the slope and b is the y-intercept.
Given that the slope (m) is ⅓ and the function must pass through the point (-15, -13), we can plug these values into the slope-point form of a linear equation to find the y-intercept (b):
f(x) = mx + b
f(-15) = ⅓(-15) + b
-13 = -9 + b
b = -13 + 9
b = -4
Now that we know the slope and y-intercept, we can write the function as:
f(x) = ⅓x - 4