Section 3.1 : Graphing
4. Determine the \(x\)-intercepts and the \(y\)-intercepts for the following equation.
\[3x - 7y = 10\]Show All Steps Hide All Steps
Start SolutionRecall that in order to find the \(y\)-intercept all we need to do is plug \(x = 0\) into the equation and solve for \(y\). Doing that for this equation gives,
\[\begin{align*}3\left( 0 \right) - 7y & = 10\\ - 7y & = 10\\ y & = - \frac{{10}}{7}\end{align*}\]The \(y\)-intercept for this equation is then the point : \(\left( {0, - \frac{{10}}{7}} \right)\) .
Show Step 2Finding the \(x\)-intercept is similar to the \(y\)-intercept. All we do is plug in \(y = 0\) and solve for \(x\). Doing that for this equation gives,
\[\begin{align*}3x - 7\left( 0 \right) & = 10\\ 3x & = 10\\ x & = \frac{{10}}{3}\end{align*}\]The \(x\)-intercept for this equation is then the point : \(\left( {\frac{{10}}{3},0} \right)\) .