Q54. - Algebra 2

Question

What is the slope of the line shown in the graph at the right?

  (A) $-\frac{\mathbf{3}}{\mathbf{2}}$                        (B) $-\frac{\mathbf{2}}{\mathbf{3}}$                 (C) $\frac{\mathbf{2}}{\mathbf{3}}$                  (D) $\frac{\mathbf{3}}{\mathbf{2}}$

Step-by-Step Solution

Answer

The slope of the given straight line is $\frac{3}{2}$. So, (D) is the correct option.

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 clear, from the given graph, that the line passes through $\left(4,-2\right)$ and $\left(6,1\right)$.

Then, $\left(h,k\right)=\left(4,-2\right)$ and $\left(a,b\right)=\left(6,1\right)$.

Step 3 – Find the slope

Put $\left(h,k\right)=\left(4,-2\right)$ and $\left(a,b\right)=\left(6,1\right)$ in $m=\frac{b-k}{a-h}$ to get,

 $\begin{array}{c}m=\frac{1-\left(-2\right)}{6-4}\\ =\frac{1+2}{2}\\ =\frac{3}{2}\end{array}$

So, $m=\frac{3}{2}$

So, the slope of the given straight line is $\frac{3}{2}$.