Solutions

1. \({\text{y}}=-4{\text{x}}-14\)


2. \({\text{y}}=\frac{1}{3}{\text{x}}+7\)


3. \({\text{y}}=\frac{1}{8}{\text{x}}-\frac{3}{8}\)


4. \({\text{y}}=9{\text{x}}-36\) (Written Solution)

   To change the equation into slope-intercept form, we write it in the form \({\text{y=mx+b}}\).

   Start with the original equation:

   \({\text{x}}=\frac{{\text{y}}+36}{9}\)

   We want to isolate the y, so our first step is to multiply both sides by 9.

   \(9{\text{x}}=\left(\frac{{\text{y}}+36}{9}\right)9\)

   Then cancel out the 9’s on the right side.

   \(9{\text{x}}=\left(\frac{{\text{y}}+36}{\:\cancel{9}}\right)\:\cancel{9}\)

   Which gives us:

   \({\text{9x=y+36}}\)

   Then subtract 36 from both sides.

   \(9{\text{x}} {\color{Red}{-}36} = {\text{y}} + 36 {\color{Red}{-}36}\)

   Which simplifies to:

   \(9{\text{x}}{-}36={\text{y}}\)

   Which is the same equation as:

   \({\text{y}}=9{\text{x}}-36\)



5. \({\text{y}}=-3{\text{x}}+\frac{7}{2}\) (Written Solution)

   To change the equation into slope-intercept form, we need to write it in the form

   \({\text{y=mx+b}}\)

   Start with our original equation:

   \(-6{\text{x}}{-}{2}\text{y}=-7\)

   We want to isolate the term with y, so we add \(6{\text{x}}\) to both sides:

   \(-6\text{x}+6{\text{x}}{-}{2}\text{y}=-7+6\text{x}\)

   Then simplify to:

   \(-2\text{y}=-7+6\text{x}\)

   Now we can multiply both sides by \({\color{Red} -\frac{1}{2}}\) (or divide by \(-2\) which is an equivalent operation).

   \({\color{Red} -\frac{1}{2}}\left ( -2\text{y} \right )= {\color{Red} -\frac{1}{2}}\left ( -7+6\text{x} \right )\)

   Multiply on the left and distribute on the right to get:

   \({\color{Red}1}\text{y}= {\color{Red} -\frac{1}{2}}\left (-7 \right )+{\color{Red} -\frac{1}{2}}\left (6\text{x} \right )\)

   Which gives us:

   \({\text{y}}=\frac{7}{2}-\frac{6}{2}{\text{x}}\)

   Which simplifies to:

   \({\text{y}}=\frac{7}{2}-{\color{Red} 3}{\text{x}}\)

   Then we can rewrite the equation so that it is in slope-intercept form:

   \({\text{y}}=-3{\text{x}}+\frac{7}{2}\)



6. \({\text{y}}=\frac{3}{2}{\text{x}}+\frac{1}{2}\)