Write the equation of the linear function that models the relationship shown in the table. Enter your answer in y = mx + b
x, y
11, 58
20, 103
First, we need to find the slope (m) of the line using the formula:
m = (y2 - y1) / (x2 - x1)
Using the values from the table, we get:
m = (103 - 58) / (20 - 11)
m = 45 / 9
m = 5
Now we can use the slope-intercept form of a line, y = mx + b, and substitute the slope we just found and one of the points from the table (let's use point (11, 58)):
y = 5x + b
Solving for b, we plug in the x and y values from point (11, 58):
58 = 5(11) + b
b = 58 - 55
b = 3
The equation of the linear function that models the relationship is:
y = 5x + 3
To find the equation of the linear function that models the relationship shown in the table, we need to determine the values of "m" (the slope) and "b" (the y-intercept).
Slope (m) can be calculated using the formula:
m = (change in y) / (change in x)
First, let's calculate the change in y and change in x:
Change in y = 103 - 58 = 45
Change in x = 20 - 11 = 9
Now we can find the slope:
m = 45 / 9 = 5
Next, we need to find the y-intercept (b).
Using the equation y = mx + b, we can substitute the values of x and y from any given point. Let's use the point (11, 58):
58 = 5(11) + b
58 = 55 + b
b = 58 - 55
b = 3
Finally, we can write the equation of the linear function in the form y = mx + b:
y = 5x + 3