Transform the linear equation −2y=14−6x

Question

to slope-intercept form.

Answer 1

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 2

what does y equal?

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!