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:
\[ y = \frac{6x - 18}{3} \]
\[ y = 2x - 6 \]
So, the equation in slope-intercept form is:
\[ y = 2x - 6 \]
Here, the slope \( m \) is 2, and the y-intercept \( b \) is -6.
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 \( y \):
Start with the original equation:
\[ 9 + 272x = -32y \]
Rearrange the equation to isolate \( y \) on one side. First, subtract \( 9 \) and then divide by \( -32 \):
\[ -32y = 272x + 9 \]
Divide every term by \( -32 \):
\[ y = -\frac{272}{32}x - \frac{9}{32} \]
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:
The y-intercept as an ordered pair is:
\[ \left(0, -\frac{9}{32}\right) \]
In summary:
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.
Start with the original equation:
\[ 9 + \frac{27}{2}x = -\frac{3}{2}y \]
Rearrange the equation to isolate \( y \). First, move all terms involving \( y \) to one side:
\[ -\frac{3}{2}y = \frac{27}{2}x + 9 \]
To isolate \( y \), multiply every term by \(-\frac{2}{3}\) to solve for \( y \):
\[ y = -\frac{2}{3} \left( \frac{27}{2}x + 9 \right) \]
Distribute \(-\frac{2}{3}\):
\[ y = -\frac{2}{3} \cdot \frac{27}{2}x - \frac{2}{3} \cdot 9 \]
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:
\[ y = -9x - 6 \]
From the equation \( y = -9x - 6 \):
As an ordered pair, the y-intercept is:
\[ (0, -6) \]
To transform the linear equation \( 4x - 8y = 24 \) into slope-intercept form (\( y = mx + b \)), we need to isolate \( y \). Here are the steps:
Start with the original equation:
\[ 4x - 8y = 24 \]
Rearrange the equation to isolate \(-8y\) on one side. Subtract \(4x\) from both sides:
\[ -8y = -4x + 24 \]
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:
\[ y = \frac{1}{2}x - 3 \]
\( y = \frac{1}{2}x - 3 \)
To write the equation \( y - 2 = 32(x + 2) \) in slope-intercept form (\( y = mx + b \)), follow these steps:
\[ y - 2 = 32x + 64 \]
\[ y = 32x + 64 + 2 \]
\[ y = 32x + 66 \]
Now the equation is in slope-intercept form, where the slope \( m = 32 \) and the y-intercept \( b = 66 \).
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!
To convert the equation \( y - 2 = \frac{3}{2}(x + 2) \) into slope-intercept form (\( y = mx + b \)), follow these steps:
\[ y - 2 = \frac{3}{2}x + \frac{3}{2} \cdot 2 \]
Calculate \(\frac{3}{2} \cdot 2\):
\[ \frac{3}{2} \cdot 2 = 3 \]
So we have:
\[ y - 2 = \frac{3}{2}x + 3 \]
\[ y = \frac{3}{2}x + 3 + 2 \]
\[ y = \frac{3}{2}x + 5 \]
Now the equation is in slope-intercept form, where the slope \( m = \frac{3}{2} \) and the y-intercept \( b = 5 \).
The slope-intercept form is:
\[ y = \frac{3}{2}x + 5 \]
From the provided responses, the correct answer is:
\(y = \frac{3}{2}x + 5\).
