Question

HELP: Find the equation of the linear function represented by the table below in slope-intercept form. (image included)

Answer 1

Given:

The table of value of a linear function.

To find:

The linear function in slope intercept form.

Solution:

Slope intercept form:

$y=mx+b$

Where, m is slope and b is y-intercept.

Consider any two points from the given table.

It is clear that the linear function passes through the points (1,0) and (2,5). So, the equation of the linear function is

$y-y_1=\dfrac{y_2-y_1}{x_2-x_1}(x-x_1)$

$y-0=\dfrac{5-0}{2-1}(x-1)$

$y=\dfrac{5}{1}(x-1)$

$y=5(x-1)$

Using distributive property, we get

$y=5(x)+5(-1)$

$y=5x-5$

Therefore, the slope intercept form of the given linear function is $y=5x-5$.