Question

or
Rewrite the following equation in slope-intercept form.

3x + 14y = 2


Write your answer using integers, proper fractions, and improper fractions in simplest form.

Answer 1

To rewrite the equation \(3x + 14y = 2\) in slope-intercept form, we want to solve for \(y\) in terms of \(x\). The slope-intercept form is given by:

\[
y = mx + b
\]

where \(m\) is the slope and \(b\) is the y-intercept.

Starting with the original equation:

\[
3x + 14y = 2
\]

First, isolate the \(y\) term by subtracting \(3x\) from both sides:

\[
14y = -3x + 2
\]

Next, divide every term by \(14\) to solve for \(y\):

\[
y = -\frac{3}{14}x + \frac{2}{14}
\]

Simplifying \(\frac{2}{14}\):

\[
\frac{2}{14} = \frac{1}{7}
\]

Now we can write the equation in slope-intercept form:

\[
y = -\frac{3}{14}x + \frac{1}{7}
\]

Thus, the equation \(3x + 14y = 2\) in slope-intercept form is:

\[
y = -\frac{3}{14}x + \frac{1}{7}
\]