Question

How do I rewrite the equation 2x + 5y = 11 in slope-intercept form?

Answer 1

To rewrite the equation \(2x + 5y = 11\) in slope-intercept form (which is \(y = mx + b\), where \(m\) is the slope and \(b\) is the y-intercept), you need to solve for \(y\).

Here are the steps:

1. Start with the original equation:
\[
2x + 5y = 11
\]

2. Subtract \(2x\) from both sides to isolate the term containing \(y\):
\[
5y = 11 - 2x
\]

3. Rearrange the equation to place the \(x\) term first:
\[
5y = -2x + 11
\]

4. Divide every term by \(5\) to solve for \(y\):
\[
y = -\frac{2}{5}x + \frac{11}{5}
\]

Now, the equation is in slope-intercept form, where the slope \(m\) is \(-\frac{2}{5}\) and the y-intercept \(b\) is \(\frac{11}{5}\). Thus, the final result is:
\[
y = -\frac{2}{5}x + \frac{11}{5}
\]