Question

Given the table below, write a linear equation that defines the dependent variable, c, in terms of the independent variable, a.

Answer 1

For a linear equation, the first step is to find the slope.

Based on the table, I see that every time "t" increases by 1, then "k" increases by 4.

Since we're told k is the dependent variable, the slope will be

`\frac{\text{change in }k}{\text{change in }t}} = (4)/(1) = 4`

The slope is always
`\frac{\text{change in dependent variable}}{\text{change in independent variable}}`.

Once you have the slope, you need the vertical (We'd normally call this this y-intercept, but there's no "y" here. You could call it the "k" intercept in this example.)

From the table, we again see that t=0 has k=2, so that 2 is the value we need.

This gives us our equation: k = 4t + 2.

(This all is really just the slope-intercept form with x's now being called "t" and y's now being called "k".)