Question

write the equation for the table given. the table has x and y values: x=0,y=0; x=2,y=16; x=4,y=32; x=6,y=48; x=8,y=64. options: y = 16/2x; y=8x; y=12x

Explanation:

Step1: Find slope with two points

Take $(x_1,y_1)=(0,0)$ and $(x_2,y_2)=(2,16)$. Slope $m=\frac{y_2-y_1}{x_2-x_1}=\frac{16-0}{2-0}=8$

Step2: Verify slope with other points

Check $(4,32)$: $m=\frac{32-16}{4-2}=\frac{16}{2}=8$. Check $(6,48)$: $m=\frac{48-32}{6-4}=\frac{16}{2}=8$

Step3: Confirm linear equation form

Since the line passes through $(0,0)$, y-intercept $b=0$. Equation is $y=mx+b=8x+0$

Step4: Simplify first option for check

$\frac{16}{2}x=8x$, but written as $y=\frac{16}{2x}$ it is not linear, so invalid.

Answer:

B. $y=8x$