Question

Given the table for the linear function k, find the equation for the function.

Answer 1

Given:

Table for the linear function k.

To find:

The equation for the function.

Solution:

Take any two points from the table.

Let the points are (10, 18) and (30, 58).

Slope of the line:

$m=\frac{y_2-y_1}{x_2-x_1}$

Here, $x_1=10, y_1=18, x_2=30, y_2=58$

$m=\frac{58-18}{30-10}$

$m=\frac{40}{20}$

m = 2

Using point-slope formula:

$y-y_1=m(x-x_1)$

$y-18=2(x-10)$

$y-18=2x-20$

Add 18 on both sides.

$y-18+18=2x-20+18$

$y=2x-2$

Replace x by c and y by k.

$k=2c-2$

The slope-intercept form of the equation of the function is k = 2c - 2.