Question

What is the slope of the line?
\[-3x+5y=2x+3y\]
Choose 1 answer:
Choose 1 answer:
(Choice A)
\[-1\]
A
\[-1\]
(Choice B)

\[\dfrac{5}2\]
B

\[\dfrac{5}2\]
(Choice C)
\[1\]
C
\[1\]
(Choice D)

\[-\dfrac{5}2\]
D

\[-\dfrac{5}2\]

Answer 1

To find the slope of the line given by the equation

\[
-3x + 5y = 2x + 3y,
\]

we first rearrange the equation into the slope-intercept form \(y = mx + b\), where \(m\) is the slope.

First, we simplify the equation:

\[
-3x + 5y - 2x - 3y = 0,
\]

which simplifies to

\[
(-3x - 2x) + (5y - 3y) = 0.
\]

This results in:

\[
-5x + 2y = 0.
\]

Next, we isolate \(y\):

\[
2y = 5x,
\]

and then divide both sides by 2:

\[
y = \frac{5}{2}x.
\]

From this, we can see that the slope \(m\) is \(\frac{5}{2}\).

So, the slope of the line is

\[
\boxed{\frac{5}{2}}.
\]

Thus, the correct choice is (Choice B) \(\frac{5}{2}\).