Question

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

Answer 1

To put the equation \( 12x - 20y = -40 \) into slope-intercept form (which is \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept), we will solve for \( y \).

Starting with the original equation:

\[
12x - 20y = -40
\]

1. **Isolate the term involving \( y \)**:

Subtract \( 12x \) from both sides:

\[
-20y = -12x - 40
\]

2. **Divide each term by -20** to solve for \( y \):

\[
y = \frac{-12x}{-20} + \frac{-40}{-20}
\]

Simplifying each of these fractions gives:

\[
y = \frac{12}{20} x + 2
\]

3. **Simplify the fraction \( \frac{12}{20} \)**:

The greatest common divisor of 12 and 20 is 4, so:

\[
\frac{12}{20} = \frac{12 \div 4}{20 \div 4} = \frac{3}{5}
\]

4. **Write the final slope-intercept form**:

Thus, the equation in slope-intercept form is:

\[
y = \frac{3}{5}x + 2
\]

So, the equation \( 12x - 20y = -40 \) in slope-intercept form is:

\[
y = \frac{3}{5}x + 2
\]