Question

Which of the following lines would be parallel to y=3/4x−2 ?(1 point)
Responses

4x−3y=6
4 x minus 3 y equals 6

3x−4y=8
3 x minus 4 y equals 8

4x−3y=12
4 x minus 3 y equals 12

3x−4y=12

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=−6/5x+6
y equals negative Start Fraction 6 over 5 End Fraction x plus 6

y=5/6x+6
y equals Start Fraction 5 over 6 End Fraction x plus 6



Which of the following options would be the equation of a line perpendicular to the line y=−3x+5 ?(1 point)
Responses

y=3x+9
y equals 3 x plus 9

y=−1/3x+9
y equals negative Start Fraction 1 over 3 End Fraction x plus 9

y=1/3x+9
y equals Start Fraction 1 over 3 End Fraction x plus 9

y=−3x+9


Which line is perpendicular to the line y=−7/4 and goes through the point (−7,5) ?(1 point)
Responses

y=4/7x+5
y equals Start Fraction 4 over 7 End Fraction x plus 5

y=−7/4x+5
y equals negative Start Fraction 7 over 4 End Fraction x plus 5

y=−4/7x+1
y equals negative Start Fraction 4 over 7 End Fraction x plus 1

y=4/7x+9


Choose the equation of the line that is parallel to the x-axis.(1 point)
Responses

x=7
x equals 7

y=7x
y equals 7 x

y=7
y equals 7

x=7y

Answer 1

pick one answer for one

Answer 2

Let's go through each question one by one:

1. **Which of the following lines would be parallel to \( y = \frac{3}{4}x - 2 \)?**
- The slope of the line \( y = \frac{3}{4}x - 2 \) is \( \frac{3}{4} \).
- Lines that are parallel have the same slope. We need to find which option has the same slope.
- Let's convert the lines to slope-intercept form \( y = mx + b \):
- **Option 1**: \( 4x - 3y = 6 \) -> rearranging gives \( y = \frac{4}{3}x - 2 \) (slope = \( \frac{4}{3} \))
- **Option 2**: \( 3x - 4y = 8 \) -> rearranging gives \( y = \frac{3}{4}x - 2 \) (slope = \( \frac{3}{4} \))
- **Option 3**: \( 4x - 3y = 12 \) -> rearranging gives \( y = \frac{4}{3}x - 4 \) (slope = \( \frac{4}{3} \))
- **Option 4**: \( 3x - 4y = 12 \) -> rearranging gives \( y = \frac{3}{4}x - 3 \) (slope = \( \frac{3}{4} \))
- The lines with slope \( \frac{3}{4} \) are **Option 2** and **Option 4**.

2. **Which line is parallel to the line \( y = \frac{5}{6}x \) and goes through the point \( (12,6) \)?**
- The slope of the line \( y = \frac{5}{6}x \) is \( \frac{5}{6} \).
- A parallel line will also have the slope \( \frac{5}{6} \).
- Using the point-slope form \( y - y_1 = m(x - x_1) \):
\[
y - 6 = \frac{5}{6}(x - 12)
\]
- Simplifying this gives \( y = \frac{5}{6}x - 4 \).
- The correct option is **\( y = \frac{5}{6}x - 4 \)**.

3. **Which of the following options would be the equation of a line perpendicular to the line \( y = -3x + 5 \)?**
- The slope of the line \( y = -3x + 5 \) is \( -3 \).
- The negative reciprocal (perpendicular slope) is \( \frac{1}{3} \).
- The option with slope \( \frac{1}{3} \) is:
- **Option 3**: \( y = \frac{1}{3}x + 9 \) has slope \( \frac{1}{3} \).
- The correct option is **\( y = \frac{1}{3}x + 9 \)**.

4. **Which line is perpendicular to the line \( y = -\frac{7}{4} \) and goes through the point \( (-7, 5) \)?**
- The line \( y = -\frac{7}{4} \) is a horizontal line with slope \( 0 \).
- A line perpendicular to a horizontal line is vertical and has an undefined slope. The line equation would be \( x = -7 \).
- However, only slope information was used, and the question did not offer a vertical option. Let's go through the candidates:
- The lines given contain the slope \( \frac{4}{7} \), and we need a vertical line.
- The line **\( y = \frac{4}{7}x + 5 \)** has slope \( \frac{4}{7} \), which could imply that this is the most relevant option if we assume match from the context.
- We don’t have a defining option here, but the other choices do not fit the context of perpendicularity.

5. **Choose the equation of the line that is parallel to the x-axis.**
- A line parallel to the x-axis has the format \( y = k \) (where \( k \) is some constant).
- The correct option is **\( y = 7 \)**.

So the final answers are:
1. Options 2 and 4 are parallel.
2. \( y = \frac{5}{6}x - 4 \)
3. \( y = \frac{1}{3}x + 9 \)
4. The context didn't suitably answer.
5. \( y = 7 \)

Answer 3

Certainly! Here are the single answers for each question:

1. **Which of the following lines would be parallel to \( y = \frac{3}{4}x - 2 \)?**
- **Answer:** \( 3x - 4y = 8 \) (Option 2)

2. **Which line is parallel to the line \( y = \frac{5}{6}x \) and goes through the point \( (12,6) \)?**
- **Answer:** \( y = \frac{5}{6}x - 4 \)

3. **Which of the following options would be the equation of a line perpendicular to the line \( y = -3x + 5 \)?**
- **Answer:** \( y = \frac{1}{3}x + 9 \)

4. **Which line is perpendicular to the line \( y = -\frac{7}{4} \) and goes through the point \( (-7,5) \)?**
- **Answer:** \( y = \frac{4}{7}x + 5 \)

5. **Choose the equation of the line that is parallel to the x-axis.**
- **Answer:** \( y = 7 \)

If you need any further clarification or additional questions, feel free to ask!