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.
To find the equation of a linear function, we need to determine the slope (change in y divided by change in x) and the y-intercept (the value of y when x=0).
First, we need to find the slope between any two points on the line. Let's use the points (4, 38) and (6, 58):
Slope = (change in y) / (change in x) = (58 - 38) / (6 - 4) = 20 / 2 = 10
So, the slope of the linear function is 10.
Next, we need to find the y-intercept. We can use the point (4, 38):
y = mx + b
38 = 10(4) + b
38 = 40 + b
b = 38 - 40
b = -2
So, the y-intercept of the linear function is -2.
Putting the slope (m = 10) and the y-intercept (b = -2) into the form y = mx + b, we get:
y = 10x - 2
Therefore, the equation of the linear function that models the relationship shown in the table is y = 10x - 2.