Question

Which of the following lines would be parallel to y=34x−2 ?(1 point)

A: 4x - 3y = 6

B: 3x - 4y = 12

C: 4x - 3y = 12

D: 3x-4y = 8

Answer 1

clearly, the user meant y = 3/4 x - 2
so, choices B.D are correct

Answer 2

To determine which of the given lines is parallel to the line \( y = 34x - 2 \), we need to identify the slope of that line. The slope-intercept form of a linear equation is given by \( y = mx + b \), where \( m \) is the slope.

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

Now, let's rewrite each of the given options in slope-intercept form (\( y = mx + b \)) to find their slopes:

**Option A:**
\( 4x - 3y = 6 \)
Rearranging gives:
\(-3y = -4x + 6\)
Dividing everything by -3:
\( y = \frac{4}{3}x - 2 \)
Slope = \( \frac{4}{3} \)

**Option B:**
\( 3x - 4y = 12 \)
Rearranging gives:
\(-4y = -3x + 12\)
Dividing everything by -4:
\( y = \frac{3}{4}x - 3 \)
Slope = \( \frac{3}{4} \)

**Option C:**
\( 4x - 3y = 12 \)
Rearranging gives:
\(-3y = -4x + 12\)
Dividing everything by -3:
\( y = \frac{4}{3}x - 4 \)
Slope = \( \frac{4}{3} \)

**Option D:**
\( 3x - 4y = 8 \)
Rearranging gives:
\(-4y = -3x + 8\)
Dividing everything by -4:
\( y = \frac{3}{4}x - 2 \)
Slope = \( \frac{3}{4} \)

Now we compare the slopes:

- Option A: \( \frac{4}{3} \)
- Option B: \( \frac{3}{4} \)
- Option C: \( \frac{4}{3} \)
- Option D: \( \frac{3}{4} \)

None of the options have a slope of \( 34 \). Therefore, none of the lines given in A, B, C, or D are parallel to the line \( y = 34x - 2 \).

Answer 3

Thank you for the clarification! If the intended line to compare against is \( y = \frac{3}{4}x - 2 \), then we need to identify which lines among the options provided have the same slope of \( \frac{3}{4} \).

The slopes from the options are:

- **Option A**: \( y = \frac{4}{3}x - 2 \) (Slope = \( \frac{4}{3} \))
- **Option B**: \( y = \frac{3}{4}x - 3 \) (Slope = \( \frac{3}{4} \))
- **Option C**: \( y = \frac{4}{3}x - 4 \) (Slope = \( \frac{4}{3} \))
- **Option D**: \( y = \frac{3}{4}x - 2 \) (Slope = \( \frac{3}{4} \))

In this case, Options B and D both have the slope \( \frac{3}{4} \) and are therefore parallel to the line \( y = \frac{3}{4}x - 2 \).

So you are correct: Options **B** and **D** are indeed parallel to the line \( y = \frac{3}{4}x - 2 \). Thank you for your patience, and I appreciate the correction!