The slope-intercept equation of a line is given by
y = mx + b
where m is the gradient, and b the intercept
So w can re-write the two equations in this form by making y the subject of the formula.
Given: 6x + 9y = 27
Step 1: make 9y the subject of the formula
9y = -6x + 27
Step 2: Divide both sides by 9
[tex]\begin{gathered} y\text{ =}\frac{-6x}{9}\text{ + }\frac{27}{9} \\ \\ y\text{ = -}\frac{2}{3}x\text{ + 3} \end{gathered}[/tex]Slope Equation of the first equation => y = -2x/3 + 3
For the second equation
Given: 7x = 3y - 12
Step 1: make 3y the subject of the formula
3y = 7x + 12
step 2: Divide both sides by 3
[tex]\begin{gathered} y\text{ =}\frac{7x}{3}\text{ + }\frac{12}{3} \\ \\ y\text{ =}\frac{7x}{3}\text{ + 4} \end{gathered}[/tex]Slope Equation of the first equation => y = -2x/3 + 3
The slope equation of the second equation is => y = 7x/3 + 4
