Write the linear equation 3y=6x−18

in slope-intercept form.(1 point) .

11 answers

To convert the equation \( 3y = 6x - 18 \) into slope-intercept form (which is \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept), you can follow these steps:

  1. Divide both sides of the equation by 3 to isolate \( y \):

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

  1. Simplify the right-hand side:

\[ y = 2x - 6 \]

So, the equation in slope-intercept form is:

\[ y = 2x - 6 \]

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

What is the slope and the y
-intercept of the equation 9+272x=−32y
. Write the y
-intercept as an ordered pair.(1 point)

To find the slope and y-intercept of the equation \( 9 + 272x = -32y \), we first need to write it in slope-intercept form, which is \( y = mx + b \).

Here are the steps to isolate \( y \):

  1. Start with the original equation:

    \[ 9 + 272x = -32y \]

  2. Rearrange the equation to isolate \( y \) on one side. First, subtract \( 9 \) and then divide by \( -32 \):

    \[ -32y = 272x + 9 \]

  3. Divide every term by \( -32 \):

    \[ y = -\frac{272}{32}x - \frac{9}{32} \]

  4. Simplify the fraction \( -\frac{272}{32} \):

    \[ -\frac{272}{32} = -8.5 \]

Thus, the equation can be written as:

\[ y = -8.5x - \frac{9}{32} \]

Now we can identify the slope and the y-intercept:

  • Slope \( m = -8.5 \)
  • y-intercept \( b = -\frac{9}{32} \)

The y-intercept as an ordered pair is:

\[ \left(0, -\frac{9}{32}\right) \]

In summary:

  • Slope: \( -8.5 \)
  • y-intercept: \( \left(0, -\frac{9}{32}\right) \)
What is the slope and the y
-intercept of the equation 9 + 27/2x = −3/2y
. Write the y
-intercept as an ordered pair.(1 point)

To find the slope and the y-intercept of the equation \( 9 + \frac{27}{2}x = -\frac{3}{2}y \), we will first rearrange it into slope-intercept form \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept.

Steps to rearrange the equation:

  1. Start with the original equation:

    \[ 9 + \frac{27}{2}x = -\frac{3}{2}y \]

  2. Rearrange the equation to isolate \( y \). First, move all terms involving \( y \) to one side:

    \[ -\frac{3}{2}y = \frac{27}{2}x + 9 \]

  3. To isolate \( y \), multiply every term by \(-\frac{2}{3}\) to solve for \( y \):

    \[ y = -\frac{2}{3} \left( \frac{27}{2}x + 9 \right) \]

  4. Distribute \(-\frac{2}{3}\):

    \[ y = -\frac{2}{3} \cdot \frac{27}{2}x - \frac{2}{3} \cdot 9 \]

  5. Simplify both terms:

    • The first term simplifies as follows: \[ y = -\frac{27}{3}x = -9x \]

    • The second term simplifies as follows: \[ -\frac{2 \cdot 9}{3} = -6 \]

So now we have:

\[ y = -9x - 6 \]

Identifying the Slope and Y-Intercept:

From the equation \( y = -9x - 6 \):

  • Slope \( m = -9 \)
  • Y-intercept \( b = -6 \)

As an ordered pair, the y-intercept is:

\[ (0, -6) \]

Summary:

  • Slope: \( -9 \)
  • Y-intercept: \( (0, -6) \)
Transform the linear equation 4x−8y=24 to slope-intercept form.(1 point)
Responses

−8y=−4x+24
negative 8 y equals negative 4 x plus 24

4x−8y=24
4 x minus 8 y equals 24

y=12x−3
y equals Start Fraction 1 over 2 End Fraction x minus 3

4x−8y−24=0

To transform the linear equation \( 4x - 8y = 24 \) into slope-intercept form (\( y = mx + b \)), we need to isolate \( y \). Here are the steps:

  1. Start with the original equation:

    \[ 4x - 8y = 24 \]

  2. Rearrange the equation to isolate \(-8y\) on one side. Subtract \(4x\) from both sides:

    \[ -8y = -4x + 24 \]

  3. Now, divide every term by \(-8\) to solve for \(y\):

    \[ y = \frac{-4x + 24}{-8} \]

    This simplifies to:

    \[ y = \frac{4}{8}x - \frac{24}{8} \]

    Further simplifying gives:

    \[ y = \frac{1}{2}x - 3 \]

Thus, the equation in slope-intercept form is:

\[ y = \frac{1}{2}x - 3 \]

Conclusion:

  • The correct response from your options that represents the slope-intercept form is:

\( y = \frac{1}{2}x - 3 \)

Write y−2=32(x+2) in slope-intercept form.(1 point)
Responses

y=32x+5
y equals Start Fraction 3 over 2 End Fraction x plus 5

y=32+5x
y equals Start Fraction 3 over 2 End Fraction plus 5 x

y=32x+32
y equals Start Fraction 3 over 2 End Fraction x plus Start Fraction 3 over 2 End Fraction

y=32x+6

To write the equation \( y - 2 = 32(x + 2) \) in slope-intercept form (\( y = mx + b \)), follow these steps:

Step 1: Distribute the 32 on the right side

\[ y - 2 = 32x + 64 \]

Step 2: Add 2 to both sides to isolate \( y \)

\[ y = 32x + 64 + 2 \]

\[ y = 32x + 66 \]

Now the equation is in slope-intercept form, where the slope \( m = 32 \) and the y-intercept \( b = 66 \).

Conclusion:

The slope-intercept form is:

\[ y = 32x + 66 \]

From the provided responses, none seem to match this result. If you have any other options or need additional help, feel free to ask!

Write y−2=3/2(x+2) in slope-intercept form.(1 point)
Responses

y=32x+5
y equals Start Fraction 3 over 2 End Fraction x plus 5

y=32+5x
y equals Start Fraction 3 over 2 End Fraction plus 5 x

y=32x+32
y equals Start Fraction 3 over 2 End Fraction x plus Start Fraction 3 over 2 End Fraction

y=32x+6

To convert the equation \( y - 2 = \frac{3}{2}(x + 2) \) into slope-intercept form (\( y = mx + b \)), follow these steps:

Step 1: Distribute \(\frac{3}{2}\) on the right side

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

Calculate \(\frac{3}{2} \cdot 2\):

\[ \frac{3}{2} \cdot 2 = 3 \]

So we have:

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

Step 2: Add 2 to both sides to isolate \( y \)

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

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

Now the equation is in slope-intercept form, where the slope \( m = \frac{3}{2} \) and the y-intercept \( b = 5 \).

Conclusion:

The slope-intercept form is:

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

From the provided responses, the correct answer is:

\(y = \frac{3}{2}x + 5\).