equation of a line into slope -intercept 4x+6y=36

To convert the equation \(4x + 6y = 36\) 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 />\[4x + 6y = 36\]<br /><br />First, isolate \(6y\) by subtracting \(4x\) from both sides:<br />\[6y = -4x + 36\]<br /><br />Next, divide every term by 6 to solve for \(y\):<br />\[y = -\frac{4}{6}x + \frac{36}{6}\]<br /><br />Simplify the fractions:<br />\[y = -\frac{2}{3}x + 6\]<br /><br />So, the equation in slope-intercept form is:<br />\[y = -\frac{2}{3}x + 6\]<br /><br />Here, the slope \(m\) is \(-\frac{2}{3}\) and the y-intercept \(b\) is 6.