Question

Use the table to answer the question.
x y
4 38
6 58

Write the equation of the linear function that models the relationship shown in the table.

Answer 1

To find the equation of the linear function, we need to find the slope (m) and the y-intercept (b) of the function.

First, calculate the slope using the formula:

m = (y2 - y1) / (x2 - x1),

where (x1, y1) = (4, 38) and (x2, y2) = (6, 58).

m = (58 - 38) / (6 - 4)
m = 20 / 2
m = 10

Now that we have the slope, we can use the point-slope form of the linear equation:

y - y1 = m(x - x1)

Using the point (4, 38):

y - 38 = 10(x - 4)

Now simplify and solve for y:

y - 38 = 10x - 40
y = 10x - 2

Therefore, the equation of the linear function that models the relationship shown in the table is y = 10x - 2.