Question

What is the slope of the line parallel to the equation $2y - 3x = 2$?
A). $\dfrac{3}{2}$
B). $\dfrac{1}{2}$
C). $\dfrac{4}{2}$
D). $\dfrac{{ - 3}}{2}$

Answer 1

First, we need to know about the concept of the slope and then we will use that to apply in the line parallel to the given equation. So, we will convert the given equation to the slope-intercept form, so that we will easily find the slope value. We know that the parallel lines have the same slope. Hence, we will get the answer to the given problem once we find the slope of the given equation.
Formula used: formula of the slope-intercept form of the line is $y = mx + c$

Complete step-by-step solution:
Since from the given, that line parallels the equation $2y - 3x = 2$ and we will need to find its slope value.
We know that from the given formula of the slope-intercept form of the line is $y = mx + c$ where $m$ represents the slope of the line, $c$ is the intercept point with the y-axis.
Hence, we will change the given equation in the form of the slope-intercept.
First, convert the $x$ values on the right side we get $2y - 3x = 2 \Rightarrow 2y = 2 + 3x$
Now divide all the values with the number $2$ then we get $\dfrac{{2y}}{2} = \dfrac{2}{2} + \dfrac{{3x}}{2}$
Therefore, we have $y = \dfrac{3}{2}x + 1$ and hence we get the slope of the given equation as $m = \dfrac{3}{2}$ (comparing the equation and given formula). Here we know that if two lines are parallel then they have same slope, So the Slope of a parallel line to the given line will also be equal to $\dfrac{3}{2}$.
Thus, option A) $\dfrac{3}{2}$ is correct.

Note: Note that the parallel lines have the same slope because the slope is a measurement of the angle of the line from the horizontal since parallel lines have the same angle, and that’s why parallel lines have the same slope and we said that the same slope is parallel.