Q. 58 - Algebra 2

Question

Find the slope of the line that passes through each pair of points. (Lesson 2-3)

$\left(\mathbf{1},-\mathbf{3}\right)$, $\left(\mathbf{3},\mathbf{3}\right)$

Step-by-Step Solution

Answer

The slope of the required straight line is 3.

Step 1. State the concept

The slope of a straight-line passing through the points $\left(h,k\right)$ and $\left(a,b\right)$ is given as $m=\frac{b-k}{a-h}$.

Step 2. List the given data

It is given that the line passes through $\left(1,-3\right)$ and $\left(3,3\right)$.

Then, $\left(h,k\right)=\left(1,-3\right)$ and $\left(a,b\right)=\left(3,3\right)$.

Step 3. Find the slope

Put $\left(h,k\right)=\left(1,-3\right)$ and $\left(a,b\right)=\left(3,3\right)$ in $m=\frac{b-k}{a-h}$ to get,

$\begin{array}{c}m=\frac{3-\left(-3\right)}{3-1}\\ =\frac{3+3}{2}\\ =\frac{6}{2}\\ =3\end{array}$

So, $m=3$

So, the slope of the required straight line is 3.