Question

Find the equation of the line through the followingpair of points: (2, -10) and (4, -7).

Answer 1

Lets find the slope first:

Slope (m) is change in y's by change in x's

Change in y: -7 - - 10 = -7 + 10 = 3

Change in x: 4 - 2 = 2

Slope = 3/2 (this is m)

So, the equation is:

$\begin{gathered} y=mx+b \\ y=\frac{3}{2}x+b \end{gathered}$

b is the y-intercept.

We can get it by plugging in any point. Let's put (2, -10). So we have:

$\begin{gathered} y=\frac{3}{2}x+b \\ -10=\frac{3}{2}(2)+b \\ -10=3+b \\ b=-10-3 \\ b=-13 \end{gathered}$

Final equation is:

$\begin{gathered} y=\frac{3}{2}x+b \\ y=\frac{3}{2}x-13 \end{gathered}$