Question

Write the linear equation 3y = 6x - 18 in slope-intercept form.
__

Answer 1

To write the equation \(3y = 6x - 18\) in slope-intercept form, we need to solve for \(y\). The slope-intercept form of a linear equation is \(y = mx + b\), where \(m\) is the slope and \(b\) is the y-intercept.

Starting with the original equation:

\[
3y = 6x - 18
\]

We will divide each term by 3 to isolate \(y\):

\[
y = \frac{6x}{3} - \frac{18}{3}
\]

This simplifies to:

\[
y = 2x - 6
\]

Thus, the equation in slope-intercept form is:

\[
y = 2x - 6
\]

In this equation, the slope \(m\) is 2, and the y-intercept \(b\) is -6.