Question

To graph the equation 2x + 5y = 10, Zeplyn draws a line through the points (5, 0) and (0, 2). What is the slope of the line represented by 2x + 5y = 10?

negative StartFraction 5 Over 2 EndFraction
negative StartFraction 2 Over 5 EndFraction
StartFraction 2 Over 5 EndFraction
StartFraction 5 Over 2 EndFraction

Answer 1

To determine the slope of the line represented by the equation \(2x + 5y = 10\), we can first write the equation in slope-intercept form, \(y = mx + b\), where \(m\) is the slope.

Starting with the given equation:

\[
2x + 5y = 10
\]

We can solve for \(y\):

1. Subtract \(2x\) from both sides:

\[
5y = -2x + 10
\]

2. Now, divide all terms by 5:

\[
y = -\frac{2}{5}x + 2
\]

From this form, we can clearly see that the slope \(m\) of the line is:

\[
m = -\frac{2}{5}
\]

Thus, the slope of the line represented by the equation \(2x + 5y = 10\) is:

\[
\text{negative } \frac{2}{5}
\]

So the correct answer is:

\(\text{negative } \frac{2}{5}\)