Finding the Slope and y-intercept from an Equation of a Line

Find the slope \(m\) and the \(y\)-intercept of the equation \(2x+4y=8\). Graph the equation.

Solution  To obtain the slope and \(y\)-intercept, we write the equation in slope-intercept form by solving for \(y\). \begin{eqnarray*} 2x+4y &=&8 \\[3pt] 4y &=&-2x+8 \\[3pt] y &=&-\dfrac{1}{2}x+2 \quad{\color{#0066A7}{y=mx+b}} \end{eqnarray*}

A-20

The coefficient of \(x\) is the slope. The slope is \(-\dfrac{1}{2}.\) The constant \(2\) is the \(y\)-intercept, so the point \(( 0,2)\) is on the graph. Now use the slope \(-\dfrac{1}{2}.\) Starting at the point \(( 0,2)\), we move \(2\) units to the right and then \(1\) unit down to the point \((2, 1)\). We plot this point and draw a line through the two points. See Figure 29.

When two lines in the plane do not intersect, they are parallel.