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Find the equation of the line that is parallel to the line y=2/5x+1 and passes through the point (5,5) .(1 point) The line that...Asked by x
Find the equation of the line that is parallel to the line y=2/5x+1
and passes through the point (5,5)
.(1 point)
The line that is parallel to y=2/5x+1
and passes through the point (5,5)
is y=2/5x+
and passes through the point (5,5)
.(1 point)
The line that is parallel to y=2/5x+1
and passes through the point (5,5)
is y=2/5x+
Answers
Answered by
x
What value completes the equation of the line that is perpendicular to the line y=−3/4x+7
and goes through the point (6,1)
?(1 point)
The line that is perpendicular to y=−3/4x+7
and passes through the point (6,1)
is y=4/3x+
and goes through the point (6,1)
?(1 point)
The line that is perpendicular to y=−3/4x+7
and passes through the point (6,1)
is y=4/3x+
Answered by
x
Which of the following lines would be parallel to y=3/4x−2 ?(1 point)
Responses
4x−3y=12
4 x minus 3 y equals 12
3x−4y=8
3 x minus 4 y equals 8
3x−4y=12
3 x minus 4 y equals 12
4x−3y=6
Responses
4x−3y=12
4 x minus 3 y equals 12
3x−4y=8
3 x minus 4 y equals 8
3x−4y=12
3 x minus 4 y equals 12
4x−3y=6
Answered by
x
just pick 1
Answered by
x
Which line is parallel to the line y=5/6x and goes through the point (12,6)?(1 point)
Responses
6y=5x
6 y equals 5 x
y=5/6x−4
y equals Start Fraction 5 over 6 End Fraction x minus 4
y=5/6x+6
y equals Start Fraction 5 over 6 End Fraction x plus 6
y=−6/5x+6
Responses
6y=5x
6 y equals 5 x
y=5/6x−4
y equals Start Fraction 5 over 6 End Fraction x minus 4
y=5/6x+6
y equals Start Fraction 5 over 6 End Fraction x plus 6
y=−6/5x+6
Answered by
x
Which of the following options would be the equation of a line perpendicular to the line y=−3x+5?(1 point)
Responses
y=1/3x+9
y equals Start Fraction 1 over 3 End Fraction x plus 9
y=−1/3x+9
y equals negative Start Fraction 1 over 3 End Fraction x plus 9
y=3x+9
y equals 3 x plus 9
y=−3x+9
Responses
y=1/3x+9
y equals Start Fraction 1 over 3 End Fraction x plus 9
y=−1/3x+9
y equals negative Start Fraction 1 over 3 End Fraction x plus 9
y=3x+9
y equals 3 x plus 9
y=−3x+9
Answered by
GPT-4o mini
To find the equation of the line that is parallel to \( y = \frac{2}{5}x + 1 \) and passes through the point \( (5, 5) \), we first note that parallel lines have the same slope.
The slope of the given line \( y = \frac{2}{5}x + 1 \) is \( \frac{2}{5} \). Therefore, the slope of the line we want to find will also be \( \frac{2}{5} \).
Next, we can use the point-slope form of the equation of a line, which is given by:
\[
y - y_1 = m(x - x_1)
\]
where \( m \) is the slope, and \( (x_1, y_1) \) is the point through which the line passes.
In our case:
- \( m = \frac{2}{5} \)
- \( (x_1, y_1) = (5, 5) \)
Substituting these values into the point-slope form:
\[
y - 5 = \frac{2}{5}(x - 5)
\]
Now, we can simplify this equation.
First, distribute \( \frac{2}{5} \):
\[
y - 5 = \frac{2}{5}x - \frac{2}{5} \cdot 5
\]
\[
y - 5 = \frac{2}{5}x - 2
\]
Next, add 5 to both sides:
\[
y = \frac{2}{5}x - 2 + 5
\]
Simplifying further:
\[
y = \frac{2}{5}x + 3
\]
Thus, the equation of the line that is parallel to \( y = \frac{2}{5}x + 1 \) and passes through the point \( (5, 5) \) is:
\[
y = \frac{2}{5}x + 3
\]
So, filling in the blank, you get:
The line that is parallel to \( y = \frac{2}{5}x + 1 \) and passes through the point \( (5,5) \) is \( y = \frac{2}{5}x + 3 \).
The slope of the given line \( y = \frac{2}{5}x + 1 \) is \( \frac{2}{5} \). Therefore, the slope of the line we want to find will also be \( \frac{2}{5} \).
Next, we can use the point-slope form of the equation of a line, which is given by:
\[
y - y_1 = m(x - x_1)
\]
where \( m \) is the slope, and \( (x_1, y_1) \) is the point through which the line passes.
In our case:
- \( m = \frac{2}{5} \)
- \( (x_1, y_1) = (5, 5) \)
Substituting these values into the point-slope form:
\[
y - 5 = \frac{2}{5}(x - 5)
\]
Now, we can simplify this equation.
First, distribute \( \frac{2}{5} \):
\[
y - 5 = \frac{2}{5}x - \frac{2}{5} \cdot 5
\]
\[
y - 5 = \frac{2}{5}x - 2
\]
Next, add 5 to both sides:
\[
y = \frac{2}{5}x - 2 + 5
\]
Simplifying further:
\[
y = \frac{2}{5}x + 3
\]
Thus, the equation of the line that is parallel to \( y = \frac{2}{5}x + 1 \) and passes through the point \( (5, 5) \) is:
\[
y = \frac{2}{5}x + 3
\]
So, filling in the blank, you get:
The line that is parallel to \( y = \frac{2}{5}x + 1 \) and passes through the point \( (5,5) \) is \( y = \frac{2}{5}x + 3 \).
Answered by
GPT-4o mini
To find the equation of a line that is perpendicular to the line given by \( y = -\frac{3}{4}x + 7 \) and passes through the point \( (6, 1) \), we first need to determine the slope of the perpendicular line.
1. **Identify the slope of the original line**: The slope of the line \( y = -\frac{3}{4}x + 7 \) is \( -\frac{3}{4} \).
2. **Find the slope of the perpendicular line**: The slope of a line that is perpendicular to another is the negative reciprocal of the original slope. Therefore, the slope \( m \) of the perpendicular line is:
\[
m = -\frac{1}{\left(-\frac{3}{4}\right)} = \frac{4}{3}
\]
3. **Use the point-slope form**: Now we can use the point-slope form of the equation of a line, which is given by:
\[
y - y_1 = m(x - x_1)
\]
where \( (x_1, y_1) \) is the point through which the line passes, and \( m \) is the slope.
Plugging in our values:
- \( m = \frac{4}{3} \)
- \( (x_1, y_1) = (6, 1) \)
We get:
\[
y - 1 = \frac{4}{3}(x - 6)
\]
4. **Simplify the equation**:
Distributing \( \frac{4}{3} \):
\[
y - 1 = \frac{4}{3}x - \frac{4}{3} \cdot 6
\]
\[
y - 1 = \frac{4}{3}x - 8
\]
Now, add 1 to both sides:
\[
y = \frac{4}{3}x - 8 + 1
\]
\[
y = \frac{4}{3}x - 7
\]
So the value that completes the equation of the line that is perpendicular to \( y = -\frac{3}{4}x + 7 \) and passes through the point \( (6, 1) \) is:
The line that is perpendicular to \( y = -\frac{3}{4}x + 7 \) and passes through the point \( (6,1) \) is \( y = \frac{4}{3}x - 7 \).
Therefore, filling in the blank, we have:
The line that is perpendicular to \( y = -\frac{3}{4}x + 7 \) and passes through the point \( (6, 1) \) is \( y = \frac{4}{3}x - 7 \).
1. **Identify the slope of the original line**: The slope of the line \( y = -\frac{3}{4}x + 7 \) is \( -\frac{3}{4} \).
2. **Find the slope of the perpendicular line**: The slope of a line that is perpendicular to another is the negative reciprocal of the original slope. Therefore, the slope \( m \) of the perpendicular line is:
\[
m = -\frac{1}{\left(-\frac{3}{4}\right)} = \frac{4}{3}
\]
3. **Use the point-slope form**: Now we can use the point-slope form of the equation of a line, which is given by:
\[
y - y_1 = m(x - x_1)
\]
where \( (x_1, y_1) \) is the point through which the line passes, and \( m \) is the slope.
Plugging in our values:
- \( m = \frac{4}{3} \)
- \( (x_1, y_1) = (6, 1) \)
We get:
\[
y - 1 = \frac{4}{3}(x - 6)
\]
4. **Simplify the equation**:
Distributing \( \frac{4}{3} \):
\[
y - 1 = \frac{4}{3}x - \frac{4}{3} \cdot 6
\]
\[
y - 1 = \frac{4}{3}x - 8
\]
Now, add 1 to both sides:
\[
y = \frac{4}{3}x - 8 + 1
\]
\[
y = \frac{4}{3}x - 7
\]
So the value that completes the equation of the line that is perpendicular to \( y = -\frac{3}{4}x + 7 \) and passes through the point \( (6, 1) \) is:
The line that is perpendicular to \( y = -\frac{3}{4}x + 7 \) and passes through the point \( (6,1) \) is \( y = \frac{4}{3}x - 7 \).
Therefore, filling in the blank, we have:
The line that is perpendicular to \( y = -\frac{3}{4}x + 7 \) and passes through the point \( (6, 1) \) is \( y = \frac{4}{3}x - 7 \).
Answered by
GPT-4o mini
To determine which of the lines is parallel to \( y = \frac{3}{4}x - 2 \), we need to find the slope of the given line and then compare it with the slopes of the lines provided in the responses.
The slope of the line \( y = \frac{3}{4}x - 2 \) is \( \frac{3}{4} \). For a line to be parallel, it must have the same slope.
Now, let's find the slope of each of the given lines by rewriting them in slope-intercept form \( y = mx + b \) (where \( m \) is the slope).
1. **\( 4x - 3y = 12 \)**:
\[
-3y = -4x + 12 \quad \Rightarrow \quad y = \frac{4}{3}x - 4
\]
Slope: \( \frac{4}{3} \)
2. **\( 3x - 4y = 8 \)**:
\[
-4y = -3x + 8 \quad \Rightarrow \quad y = \frac{3}{4}x - 2
\]
Slope: \( \frac{3}{4} \)
3. **\( 3x - 4y = 12 \)**:
\[
-4y = -3x + 12 \quad \Rightarrow \quad y = \frac{3}{4}x - 3
\]
Slope: \( \frac{3}{4} \)
4. **\( 4x - 3y = 6 \)**:
\[
-3y = -4x + 6 \quad \Rightarrow \quad y = \frac{4}{3}x - 2
\]
Slope: \( \frac{4}{3} \)
Now that we have calculated the slopes:
- The slope of \( 4x - 3y = 12 \) is \( \frac{4}{3} \) (not parallel).
- The slope of \( 3x - 4y = 8 \) is \( \frac{3}{4} \) (parallel).
- The slope of \( 3x - 4y = 12 \) is \( \frac{3}{4} \) (parallel).
- The slope of \( 4x - 3y = 6 \) is \( \frac{4}{3} \) (not parallel).
**Conclusion**: The lines **\( 3x - 4y = 8 \)** and **\( 3x - 4y = 12 \)** are parallel to \( y = \frac{3}{4}x - 2 \).
The slope of the line \( y = \frac{3}{4}x - 2 \) is \( \frac{3}{4} \). For a line to be parallel, it must have the same slope.
Now, let's find the slope of each of the given lines by rewriting them in slope-intercept form \( y = mx + b \) (where \( m \) is the slope).
1. **\( 4x - 3y = 12 \)**:
\[
-3y = -4x + 12 \quad \Rightarrow \quad y = \frac{4}{3}x - 4
\]
Slope: \( \frac{4}{3} \)
2. **\( 3x - 4y = 8 \)**:
\[
-4y = -3x + 8 \quad \Rightarrow \quad y = \frac{3}{4}x - 2
\]
Slope: \( \frac{3}{4} \)
3. **\( 3x - 4y = 12 \)**:
\[
-4y = -3x + 12 \quad \Rightarrow \quad y = \frac{3}{4}x - 3
\]
Slope: \( \frac{3}{4} \)
4. **\( 4x - 3y = 6 \)**:
\[
-3y = -4x + 6 \quad \Rightarrow \quad y = \frac{4}{3}x - 2
\]
Slope: \( \frac{4}{3} \)
Now that we have calculated the slopes:
- The slope of \( 4x - 3y = 12 \) is \( \frac{4}{3} \) (not parallel).
- The slope of \( 3x - 4y = 8 \) is \( \frac{3}{4} \) (parallel).
- The slope of \( 3x - 4y = 12 \) is \( \frac{3}{4} \) (parallel).
- The slope of \( 4x - 3y = 6 \) is \( \frac{4}{3} \) (not parallel).
**Conclusion**: The lines **\( 3x - 4y = 8 \)** and **\( 3x - 4y = 12 \)** are parallel to \( y = \frac{3}{4}x - 2 \).
Answered by
GPT-4o mini
The line that is parallel to \( y = \frac{3}{4}x - 2 \) is:
**\( 3x - 4y = 8 \)**.
**\( 3x - 4y = 8 \)**.
Answered by
GPT-4o mini
To find a line that is parallel to \( y = \frac{5}{6}x \) and passes through the point \( (12, 6) \), we first note that parallel lines have the same slope. The slope of the line \( y = \frac{5}{6}x \) is \( \frac{5}{6} \).
Now we can use the point-slope form of the equation of a line, which is given by:
\[
y - y_1 = m(x - x_1)
\]
Where:
- \( m = \frac{5}{6} \) (the slope)
- \( (x_1, y_1) = (12, 6) \)
Substituting the known values into the point-slope form:
\[
y - 6 = \frac{5}{6}(x - 12)
\]
Let's simplify this:
1. Distribute \( \frac{5}{6} \):
\[
y - 6 = \frac{5}{6}x - \frac{5}{6} \cdot 12
\]
\[
y - 6 = \frac{5}{6}x - 10
\]
2. Add 6 to both sides:
\[
y = \frac{5}{6}x - 10 + 6
\]
\[
y = \frac{5}{6}x - 4
\]
Now, we need to check which of the provided options is correct.
The options given are:
1. \( 6y = 5x \)
2. \( y = \frac{5}{6}x - 4 \)
3. \( y = \frac{5}{6}x + 6 \)
4. \( y = -\frac{6}{5}x + 6 \)
The line that matches our result \( y = \frac{5}{6}x - 4 \) is:
**\( y = \frac{5}{6}x - 4 \)**.
Now we can use the point-slope form of the equation of a line, which is given by:
\[
y - y_1 = m(x - x_1)
\]
Where:
- \( m = \frac{5}{6} \) (the slope)
- \( (x_1, y_1) = (12, 6) \)
Substituting the known values into the point-slope form:
\[
y - 6 = \frac{5}{6}(x - 12)
\]
Let's simplify this:
1. Distribute \( \frac{5}{6} \):
\[
y - 6 = \frac{5}{6}x - \frac{5}{6} \cdot 12
\]
\[
y - 6 = \frac{5}{6}x - 10
\]
2. Add 6 to both sides:
\[
y = \frac{5}{6}x - 10 + 6
\]
\[
y = \frac{5}{6}x - 4
\]
Now, we need to check which of the provided options is correct.
The options given are:
1. \( 6y = 5x \)
2. \( y = \frac{5}{6}x - 4 \)
3. \( y = \frac{5}{6}x + 6 \)
4. \( y = -\frac{6}{5}x + 6 \)
The line that matches our result \( y = \frac{5}{6}x - 4 \) is:
**\( y = \frac{5}{6}x - 4 \)**.
Answered by
GPT-4o mini
To find the equation of a line that is **perpendicular** to the line given by \( y = -3x + 5 \), we first need to determine the slope of the original line.
1. **Identify the slope of the original line**:
The slope (\( m \)) of the line \( y = -3x + 5 \) is **-3**.
2. **Find the slope of the perpendicular line**:
The slope of a line that is perpendicular to another is the negative reciprocal of the original slope.
The negative reciprocal of \(-3\) is:
\[
m = \frac{1}{3}
\]
Now, let's look at the provided options and identify the one with the slope of \(\frac{1}{3}\):
1. **\( y = \frac{1}{3}x + 9 \)**: Slope is \(\frac{1}{3}\) (this could be our answer).
2. **\( y = -\frac{1}{3}x + 9 \)**: Slope is \(-\frac{1}{3}\).
3. **\( y = 3x + 9 \)**: Slope is \(3\).
4. **\( y = -3x + 9 \)**: Slope is \(-3\).
The only line with a slope of \(\frac{1}{3}\) is:
**\( y = \frac{1}{3}x + 9 \)**.
Thus, the answer is \( y = \frac{1}{3}x + 9 \), which is the equation of the line perpendicular to \( y = -3x + 5 \).
1. **Identify the slope of the original line**:
The slope (\( m \)) of the line \( y = -3x + 5 \) is **-3**.
2. **Find the slope of the perpendicular line**:
The slope of a line that is perpendicular to another is the negative reciprocal of the original slope.
The negative reciprocal of \(-3\) is:
\[
m = \frac{1}{3}
\]
Now, let's look at the provided options and identify the one with the slope of \(\frac{1}{3}\):
1. **\( y = \frac{1}{3}x + 9 \)**: Slope is \(\frac{1}{3}\) (this could be our answer).
2. **\( y = -\frac{1}{3}x + 9 \)**: Slope is \(-\frac{1}{3}\).
3. **\( y = 3x + 9 \)**: Slope is \(3\).
4. **\( y = -3x + 9 \)**: Slope is \(-3\).
The only line with a slope of \(\frac{1}{3}\) is:
**\( y = \frac{1}{3}x + 9 \)**.
Thus, the answer is \( y = \frac{1}{3}x + 9 \), which is the equation of the line perpendicular to \( y = -3x + 5 \).