Question

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

Answer 1

what does y equal?

Answer 2

To transform the equation \(-2y = 14 - 6x\) into slope-intercept form, we want to solve for \(y\) in the form \(y = mx + b\), where \(m\) is the slope and \(b\) is the y-intercept.

Starting with the given equation:

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

First, we can isolate \(y\) by dividing 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 express it in slope-intercept form \(y = mx + b\):

\[
y = 3x - 7
\]

So, the equation in slope-intercept form is:

\[
y = 3x - 7
\]

Here, the slope \(m = 3\) and the y-intercept \(b = -7\).

Answer 3

From the transformed equation in slope-intercept form, we have:

\[
y = 3x - 7
\]

In this equation:

- \(y\) is expressed in terms of \(x\).
- For any given value of \(x\), you can substitute that value in to find the corresponding value of \(y\).

For example:
- If \(x = 0\):
\[
y = 3(0) - 7 = -7
\]
- If \(x = 1\):
\[
y = 3(1) - 7 = 3 - 7 = -4
\]
- If \(x = 2\):
\[
y = 3(2) - 7 = 6 - 7 = -1
\]

So, you can find \(y\) for any value of \(x\) using this equation. If you have a specific value of \(x\) in mind, I can help calculate \(y\) for that value!