Question

Find the slope and y-intercept of the line with the equation –9x + 3y=54

Answer 1

To solve the exercise you can take the equation of the line from its standard form to its slope-intercept form:

`\begin{gathered} Ax+By=C\Rightarrow\text{ Standard form} \\ y=mx+b\Rightarrow\text{ Slope-intercept form} \\ \text{ Where m is the slope and b is the y-intercept} \end{gathered}`

To do this, solve for y from the given equation:

`\begin{gathered} -9x+3y=54 \\ \text{ Add 9x from both sides of the equation} \\ -9x+3y+9x=54+9x \\ 3y=54+9x \\ \text{ Divide by 3 into both sides of the equation} \\ (3y)/(3)=(54+9x)/(3) \\ y=(54)/(3)+(9x)/(3) \\ y=18+3x \\ \text{ Reordering} \\ y=3x+18 \end{gathered}`

Therefore, the slope and y-intercept of the line are

`\begin{gathered} m=3\Rightarrow\text{ slope} \\ b=18\Rightarrow\text{ y-intercept} \end{gathered}`