Question

rewrite the following equation in slope-intercept form.
10x - 15y = -4
write your answer using integers, proper fractions, and improper fractions in simplest form.

Explanation:

Step1: Isolate the y - term

We start with the equation \(10x - 15y=- 4\). First, we want to get the term with \(y\) by itself on one side. We can subtract \(10x\) from both sides of the equation.
\(10x-15y - 10x=-4 - 10x\)
Simplifying the left - hand side, the \(10x\) and \(- 10x\) cancel out, and we get \(-15y=-10x - 4\)

Step2: Solve for y

Now, we divide every term in the equation \(-15y=-10x - 4\) by \(-15\) to solve for \(y\).
\(y=\frac{-10x}{-15}+\frac{-4}{-15}\)
Simplify each fraction. For \(\frac{-10x}{-15}\), we can divide the numerator and denominator by their greatest common divisor, which is 5. So \(\frac{-10x\div(- 5)}{-15\div(-5)}=\frac{2x}{3}\). And \(\frac{-4}{-15}=\frac{4}{15}\)
So \(y = \frac{2}{3}x+\frac{4}{15}\)

Answer:

\(y=\frac{2}{3}x+\frac{4}{15}\)