x y
11 58
20 103
Write the equation of the linear function that models the relationship shown in the table in y= mx + b
To find the equation of the linear function, we first need to determine the values of m (the slope) and b (the y-intercept).
Using the formula for calculating the slope:
m = (y2 - y1) / (x2 - x1)
m = (103 - 58) / (20 - 11)
m = 45 / 9
m = 5
Now that we have the value of the slope, we can use it to find the y-intercept by plugging in the values of one of the points into the equation y = mx + b.
Using the point (11, 58):
58 = 5(11) + b
58 = 55 + b
b = 58 - 55
b = 3
Therefore, the equation of the linear function that models the relationship shown in the table is:
y = 5x + 3