Question

write a linear equation in slope intercept form to represent the data shown in this table.

Answer 1

Consider that a linear equation in slope intercept form is given by:

y = mx + b

where m is the slope of the line and b is the y intercept.

use the following formula to calculate the slope m:

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

where (x1,y1) and (x2,y2) are two pair of values of the table.

For (x1,y1) = (1,10) and (x2,y2) = (2,20) you have:

$m=\frac{20-10}{2-1}=10$

Next, use the same formula for m but replacing only the values of (x1,y1), just as follow:

$m=\frac{y-10}{x-1}$

and solve for y:

$\begin{gathered} (x-1)m=y-10 \\ (x-1)(10)+10=y \\ 10x-10+10=y \\ y=10x \end{gathered}$

Hence, the slope is m = 10 and the y-intercept is b = 0

Then, the linear equation is y = 10x