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Which of the following lines would be parallel to y=34x−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

1 answer

Let's go through each question step by step.

1. Which of the following lines would be parallel to \( y = 34x - 2 \)?

The slope of the line \( y = 34x - 2 \) is 34. For lines to be parallel, they must have the same slope.

We need to convert each option to slope-intercept form (y = mx + b) to check the slopes:

  1. \(4x - 3y = 6\) → Rearranging:
    \[ -3y = -4x + 6 \implies y = \frac{4}{3}x - 2 \quad \text{slope is } \frac{4}{3} \]

  2. \(3x - 4y = 8\) → Rearranging:
    \[ -4y = -3x + 8 \implies y = \frac{3}{4}x - 2 \quad \text{slope is } \frac{3}{4} \]

  3. \(4x - 3y = 12\) → Rearranging:
    \[ -3y = -4x + 12 \implies y = \frac{4}{3}x - 4 \quad \text{slope is } \frac{4}{3} \]

  4. \(3x - 4y = 12\) → Rearranging:
    \[ -4y = -3x + 12 \implies y = \frac{3}{4}x - 3 \quad \text{slope is } \frac{3}{4} \]

None of these lines have a slope of 34, so they are not parallel.

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

Lines that are parallel have the same slope. The slope is \( \frac{5}{6} \).

The equation of a line in point-slope form through (12, 6) with slope \( \frac{5}{6} \) is: \[ y - 6 = \frac{5}{6}(x - 12) \] Rearranging gives: \[ y = \frac{5}{6}x - 10 + 6 = \frac{5}{6}x - 4 \]

So the correct answer 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 given line is -3. To find a perpendicular line, we take the negative reciprocal: \[ \text{slope} = \frac{1}{3} \]

We need to find the line with a slope of \( \frac{1}{3} \):

  1. \(y = 3x + 9\) (slope = 3, NOT perpendicular)
  2. \(y = -\frac{1}{3}x + 9\) (slope = -\frac{1}{3}, NOT perpendicular)
  3. \(y = \frac{1}{3}x + 9\) (slope = \frac{1}{3, THIS IS PERPENDICULAR)
  4. \(y = -3x + 9\) (slope = -3, NOT perpendicular)

So the correct answer 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 equation \( y = -\frac{7}{4} \) is a horizontal line, which means it's parallel to the x-axis. A line that is perpendicular to a horizontal line is vertical and has the form \( x = k \).

Since the line must pass through the point \( (-7, 5) \), it would be: x = -7 (note this option is not listed but we are asked to recognize the nature of the lines).

However, based on the provided choices: None of the provided options match the requirements perfectly but from the given options, we want:

  1. \(y = \frac{4}{7}x + 5\): Not perpendicular, it's skewed.
  2. \(y = -\frac{7}{4}x + 5\): Incorrect, follows -7/4 slope, not perpendicular.
  3. \(y = -\frac{4}{7}x + 1\): Incorrect format.
  4. \(y = \frac{4}{7}x + 9\): Not applicable.

Choose the most applicable: None of the provided options seem proper.

5. Choose the equation of the line that is parallel to the x-axis.

Lines that are parallel to the x-axis have an equation of the form \( y = b \) where b is a constant.

  1. x = 7: It's a vertical line, NOT parallel to the x-axis.
  2. y = 7x: This is a line with slope, NOT parallel to x-axis.
  3. y = 7: This is a horizontal line (parallel to the x-axis).
  4. x = 7y: This is not parallel to the x-axis either.

The correct answer is: y = 7.

If there are any clarifications needed or if you need further assistance, just let me know!