Question

Question
Transform the linear equation −2y=14−6x
to slope-intercept form.

Answer 1

To transform the linear equation \(-2y = 14 - 6x\) into slope-intercept form, we need to solve for \(y\) in terms of \(x\). The slope-intercept form of a linear equation is given by \(y = mx + b\), where \(m\) is the slope and \(b\) is the y-intercept.

Starting with the equation:

\[
-2y = 14 - 6x
\]

We want to isolate \(y\). First, divide both sides of the equation by \(-2\):

\[
y = \frac{14 - 6x}{-2}
\]

Now, we can split the fraction:

\[
y = \frac{14}{-2} - \frac{6x}{-2}
\]

This simplifies to:

\[
y = -7 + 3x
\]

To put this in standard slope-intercept form \(y = mx + b\), we can rearrange it:

\[
y = 3x - 7
\]

Now, the equation in slope-intercept form is:

\[
y = 3x - 7
\]

In this equation, the slope \(m\) is \(3\) and the y-intercept \(b\) is \(-7\).