Question

which equation represents the relationship between the independent and dependent variables as shown in the table?

x	0	2	4	6	8
y	2	10	18	26	34

a. y = 5x + 2
b. y = 2x + 4
c. y = 4x + 2
d. y = 2x + 5

Explanation:

Step1: Recall slope - intercept form

The equation of a line is $y = mx + b$, where $m$ is the slope and $b$ is the y - intercept.

Step2: Find the y - intercept

When $x = 0$, from the table $y=2$. So $b = 2$.

Step3: Calculate the slope

Using two points $(x_1,y_1)=(0,2)$ and $(x_2,y_2)=(2,10)$. The slope $m=\frac{y_2 - y_1}{x_2 - x_1}=\frac{10 - 2}{2-0}=\frac{8}{2}=4$.

Step4: Determine the equation

The equation is $y = 4x+2$.

Answer:

C. $y = 4x + 2$