Put the following equation of a line into slope -intercept form, simplifying all fractions. 3x+6y=36 Answer Attemptiout of 2 square

To convert the equation \(3x + 6y = 36\) into slope-intercept form, we need 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.<br /><br />Starting with the given equation:<br />\[3x + 6y = 36\]<br /><br />1. Isolate the term involving \(y\):<br />\[6y = 36 - 3x\]<br /><br />2. Divide every term by 6 to solve for \(y\):<br />\[y = \frac{36 - 3x}{6}\]<br /><br />3. Simplify the fractions:<br />\[y = \frac{36}{6} - \frac{3x}{6}\]<br />\[y = 6 - \frac{x}{2}\]<br /><br />So, the equation in slope-intercept form is:<br />\[y = -\frac{1}{2}x + 6\]<br /><br />Thus, the simplified equation is:<br />\[y = -\frac{1}{2}x + 6\]