Question

write an equation for the line that passes through the points (6,6) and (12,9)

Answer 1

A line is represented by the following expression in slope-intercept form:

$\begin{gathered} y=mx+b \\ \text{where, } \\ m=\text{slope} \\ b=y-\text{intercept} \end{gathered}$

To get this expression, we must calculate the slope first and then use the slope-point form to finally get the slope-intercept form:

*Slope is given by this formula:

Using the two given points (6,6) and (12,9)

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

Substituting the points:

$\begin{gathered} m=\frac{9-6}{12-6} \\ m=\frac{3}{6} \\ m=\frac{1}{2} \end{gathered}$

Then, by the slope-point form, which is given by:

$y-y_1=m(x-x_1)$$\begin{gathered} y-6=\frac{1}{2}(x-6) \\ y=\frac{1}{2}x-3+6 \\ y=\frac{1}{2}x+3 \end{gathered}$