Question

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

Answer 1

Hint: To solve this problem, i.e., to find the slope of the line parallel to the given equation. We will convert the equation onto slope intercept form, from here we will get the slope of the equation. Now since the parallel lines have same slope, i.e., both will have the same slope. Hence, we will get our required answer same as the slope of the equation which we have solved earlier.

Complete step-by-step answer:
We need to find the slope of the line parallel to the equation \[2y-3x = 4.\]
We know that the slope intercept form of the line is \[y = mx + c.\]
where, m \[ = \] slope of the line
c \[ = \] y-intercept.
So, we will change the given equation \[2y - 3x = 4\] in slope intercept form.
On changing the given equation \[2y - 3x = 4\] in slope intercept form, we get
\[
\Rightarrow {2y{\text{ }} - {\text{ }}3x{\text{ }} = {\text{ }}4} \\
\Rightarrow {2y{\text{ }} = {\text{ }}3x{\text{ }} + {\text{ }}4} \\
\Rightarrow {{\text{y }} = {\text{ }}\dfrac{3}{2}x{\text{ }} + {\text{ }}2}
\]
So, we get the slope of the line \[2y - 3x = 4,\] which is $ m = \dfrac{3}{2}. $
According to the question, the slope of the line is parallel to the given equation and we know that the parallel lines have the same slope.
Hence, the slope of the line parallel to the line \[2y - 3x = 4\]is $ m = \dfrac{3}{2}. $
Thus, option (A) $ \dfrac{3}{2} $ , is correct.

So, the correct answer is “Option A”.

Note: In the solution we have mentioned that the parallel lines have same slope, because slope is a measurement of the angle of a line from the horizontal, and since parallel lines have the same angle, that’s why parallel lines have the same slope or we can say that lines with the same slope are parallel.