Write the linear equation 3y=6x−18

Question

in slope-intercept form.(1 point) .

Answer 1

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 $y$:

$$y=\frac{6x-18}{3}$$

2. 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.

Answer 2

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

Answer 3

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:

$$(0,-\frac{9}{32})$$

In summary:

• Slope: $-8.5$
• y-intercept: $(0,-\frac{9}{32})$

Answer 4

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)

Answer 5

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 $y$:

   $$y=-\frac{2}{3}(\frac{27}{2}x+9)$$

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: $(0,-6)$

Answer 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

Answer 7

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:

$y=\frac{1}{2}x-3$

Answer 8

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

Answer 9

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!

Answer 10

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

Answer 11

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:

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