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 the linear function that models the relationship shown in the table, we can use the two data points (4, 38) and (6, 58) to find the slope and y-intercept of the line.
First, calculate the slope (m) using the formula:
m = (y2 - y1) / (x2 - x1)
m = (58 - 38) / (6 - 4)
m = 20 / 2
m = 10
Now, substitute the slope value and one of the data points into the point-slope form of a linear equation:
y - y1 = m(x - x1)
y - 38 = 10(x - 4)
Next, simplify the equation:
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.