Question

Fina Question 1. Write the equation of the line that goes through the points (-2,1) and (4,2)

Answer 1

If we have two coordinates that are in the line we can find the slope with this equation:

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

So now we replace the coordinates so:

$\begin{gathered} m=\frac{2-1}{4-(-2)} \\ m=\frac{1}{6} \end{gathered}$

Now with the slope and any point we can find the intercept in the y axis by replacing x=0 so:

$\begin{gathered} \frac{1}{6}=\frac{y-2}{0-4} \\ -\frac{4}{6}=y-2 \\ -\frac{2}{3}+\frac{6}{3}=y \\ \frac{4}{3}=y \end{gathered}$

So the equation is:

$y=\frac{1}{6}x+\frac{4}{3}$