Q. 5 - Precalculus Enhanced with Graphing Utilities

Question

True or False The slope of the line $2y=3x+5$ is $3.$

Step-by-Step Solution

Answer

The statement "The slope of the line $2y=3x+5$ is $3$." is false.

Step 1. Given information.

We have:

$2y=3x+5$

Step 2. Find whether the statement is true or false.

The equation is $2y=3x+5$.

Convert the equation into slope-intercept form:

Divide both sides by $2:$

$$\begin{gathered} \frac{2y}{2}=\frac{3x+5}{2} \\ y=\frac{3}{2}x+\frac{5}{2} \end{gathered}$$

Compare the equation with slope intercept form$y=mx+b$, where $m$ is slope, we get:

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

Hence, the statement is false.