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