Question

put the following equation of a line into slope - intercept form, simplifying all fractions. 12x - 20y = -40

Explanation:

Step1: Isolate the y - term

We start with the equation \(12x - 20y=-40\). First, we want to get the term with \(y\) by itself on one side. We can do this by subtracting \(12x\) from both sides of the equation.
\(12x-20y - 12x=-40 - 12x\)
Simplifying the left - hand side, the \(12x\) and \(- 12x\) cancel out, and we get \(-20y=-12x - 40\)

Step2: Solve for y

Now, we divide every term in the equation \(-20y=-12x - 40\) by \(-20\) to solve for \(y\).
\(y=\frac{-12x}{-20}+\frac{-40}{-20}\)

Step3: Simplify the fractions

Simplify each fraction. For the first fraction, \(\frac{-12}{-20}=\frac{12}{20}=\frac{3}{5}\) (dividing both the numerator and denominator by their greatest common divisor, which is 4). For the second fraction, \(\frac{-40}{-20} = 2\).
So, \(y=\frac{3}{5}x + 2\)

Answer:

\(y=\frac{3}{5}x + 2\)