Question

5.6 linear functions in the real world
write an equation to represent the data in the table below. place your answer in slope - intercept form. do not include spaces in your answer.
x 4 5 6 7 8
y 21 28 35 42 49
y=

Explanation:

Step1: Calculate the slope

The slope $m$ formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$. Let $(x_1,y_1)=(4,21)$ and $(x_2,y_2)=(5,28)$. Then $m=\frac{28 - 21}{5 - 4}=\frac{7}{1}=7$.

Step2: Find the y - intercept

Use the slope - intercept form $y=mx + b$ and substitute $m = 7$, $x = 4$ and $y = 21$. So $21=7\times4 + b$. Then $21 = 28 + b$, and $b=21 - 28=-7$.

Answer:

$y=7x - 7$