Question

Complete the expression that represents the table

Y=___x

Answer 1

Answer:

The equation that represents the table is:

• $y=\frac{9}{2}x$

Step-by-step explanation:

Taking two points from the table

• (2, 9)

• (4, 18)

$\mathrm{Slope\:between\:two\:points}:\quad \mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}$

$\left(x_1,\:y_1\right)=\left(2,\:9\right),\:\left(x_2,\:y_2\right)=\left(4,\:18\right)$

$m=\frac{18-9}{4-2}$

$m=\frac{9}{2}$

As the slope-intercept form is

$\:y=mx+b$

Plugging (2, 9) to find the y-intercept 'b'

$9=\frac{9}{2}\left(2\right)+b$

$\mathrm{Switch\:sides}$

$\frac{9}{2}\left(2\right)+b=9$

$\mathrm{Remove\:parentheses}:\quad \left(a\right)=a$

$\frac{9}{2}\cdot \:2+b=9$

$9+b=9$

$b=0$

so the equation becomes

$\:y=mx+b$

• $m=\frac{9}{2}$

• $b=0$

$y=\frac{9}{2}\left(x\right)+0$

$y=\frac{9}{2}x$

Therefore, the equation that represents the table is:

• $y=\frac{9}{2}x$

The graph of the equation is also attached below.