Question

Write the equation in slope-intercept form. What are the slope and y-intercept? -11x+9y=-12

Answer 1

that means solve the equation for y

Answer 2

slope intercept form is \(y=mx+b\) where \(m\) is the slope and \(b\) is the y-intercept.

to convert to slope-intercept form, solve for \(y\):\[-11x+9y=-12\]add \(-11x\) to both sides to isolate the \(y\)-term:\[-11x+9y=-12\]\[\underline{\color{red}{+11x~~~~~~~~~~~+11x}}\]\[~~~~~~~0+9y=-12+11x\]divide both sides by \(9\) to isolate the \(y\) variable:\[{9y\over\color{red}{9}}={-12\over\color{red}{9}}+{11x\over\color{red}{9}}\]\[y=-{4\over3}+{11\over9}x\]To put the equation in slope-intercept order, switch the two terms on the left side:\[y={11\over9}x-{4\over3}\]Now you have the equation in slope-intercept form. From this, you should be able to identify that the slope, \(m\) is \({11\over9}\) and the y-intercept, \(b\) is \(-{4\over3}\)