Question

What is the slope of the line?
\[7x+2y=5\]
Choose 1 answer:
Choose 1 answer:
(Choice A)

\[\dfrac{7}2\]
A

\[\dfrac{7}2\]
(Choice B)

\[-\dfrac{2}7\]
B

\[-\dfrac{2}7\]
(Choice C)

\[\dfrac{2}7\]
C

\[\dfrac{2}7\]
(Choice D)

\[-\dfrac{7}2\]
D

\[-\dfrac{7}2\]

Answer 1

To find the slope of the line given by the equation \(7x + 2y = 5\), we need to rewrite the equation in slope-intercept form, which is \(y = mx + b\), where \(m\) represents the slope.

Starting with the original equation:
\[
7x + 2y = 5
\]

We can isolate \(y\) by subtracting \(7x\) from both sides:
\[
2y = -7x + 5
\]

Next, we divide every term by \(2\) to solve for \(y\):
\[
y = -\frac{7}{2}x + \frac{5}{2}
\]

Now, we have the equation in the form \(y = mx + b\). Here, the slope \(m\) is:
\[
m = -\frac{7}{2}
\]

Thus, the slope of the line is:
\[
\text{Slope} = -\frac{7}{2}
\]

So the correct choice is:
**(Choice D) \(-\frac{7}{2}\)**.