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

Question

TABLE:
(x: 4,6)
(y:38,58)

Answer 1

To find the equation of the linear function, we first need to calculate the slope (m) using the two points (4,38) and (6,58).

m = (y2 - y1) / (x2 - x1)
m = (58 - 38) / (6 - 4)
m = 20 / 2
m = 10

Next, we can use the slope-intercept form of a linear equation (y = mx + b) and one of the points to solve for the y-intercept (b).

Using the point (4,38):
38 = 10(4) + b
38 = 40 + b
b = -2

Now we have the slope (m = 10) and the y-intercept (b = -2), so the equation of the linear function is:

y = 10x - 2