Write the equation if the linear function that models the relationship shown in the table x,4,6 y,38,58
To find the equation of a linear function, we need to find the slope (m) and the y-intercept (b).
First, let's calculate the slope using the formula:
m = (change in y)/(change in x)
For x = 4 to x = 6:
(change in y) = (58 - 38) = 20
(change in x) = (6 - 4) = 2
So, the slope (m) is:
m = 20/2 = 10
Now, let's find the y-intercept (b) by substituting one set of coordinates (x, y) into the equation y = mx + b. Using the point (4, 38):
38 = (10)(4) + b
38 = 40 + b
b = 38 - 40
b = -2
Therefore, the equation of the linear function is:
y = 10x - 2