Question

write the slope intercept equations for the following lines and sketch the graph

Answer 1

Solution:

Given the points;

$(3,3)\text{ and }(6,9)$

The slope, m, of a line is;

$\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ \\ \text{ Where;} \\ \\ x_1=3,y_1=3,x_2=6,y_2=9 \end{gathered}$$\begin{gathered} m=\frac{9-3}{6-3} \\ \\ m=\frac{6}{3} \\ \\ m=2 \end{gathered}$

Thus;

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

Thus, the slope-intercept equation is;

$y=2x-3$

And the graph is;