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

Responses

3x−4y=8
3 x minus 4 y equals 8

4x−3y=12
4 x minus 3 y equals 12

3x−4y=12
3 x minus 4 y equals 12

4x−3y=6

9 answers

To determine which lines are parallel to \( y = 34x - 2 \), we first need to identify the slope of this equation. The equation is in the slope-intercept form \( y = mx + b \), where \( m \) is the slope. Here, the slope \( m = 34 \).

Lines that are parallel to each other have the same slope. Therefore, we need to find the lines in the given options that also have a slope of 34.

We can convert each of the given options to the slope-intercept form \( y = mx + b \):

  1. For \( 3x - 4y = 8 \): \[ -4y = -3x + 8 \quad \Rightarrow \quad y = \frac{3}{4}x - 2 \] (Slope = \( \frac{3}{4} \))

  2. For \( 4x - 3y = 12 \): \[ -3y = -4x + 12 \quad \Rightarrow \quad y = \frac{4}{3}x - 4 \] (Slope = \( \frac{4}{3} \))

  3. For \( 3x - 4y = 12 \): \[ -4y = -3x + 12 \quad \Rightarrow \quad y = \frac{3}{4}x - 3 \] (Slope = \( \frac{3}{4} \))

  4. For \( 4x - 3y = 6 \): \[ -3y = -4x + 6 \quad \Rightarrow \quad y = \frac{4}{3}x - 2 \] (Slope = \( \frac{4}{3} \))

Now, let's summarize the slopes from each calculation:

  • \( 3x - 4y = 8 \): Slope = \( \frac{3}{4} \)
  • \( 4x - 3y = 12 \): Slope = \( \frac{4}{3} \)
  • \( 3x - 4y = 12 \): Slope = \( \frac{3}{4} \)
  • \( 4x - 3y = 6 \): Slope = \( \frac{4}{3} \)

None of the given lines have a slope of 34, meaning none of them are parallel to the line \( y = 34x - 2 \).

you have to choose one

Apologies for the confusion! In this case, since none of the lines have the same slope as \( y = 34x - 2 \) (which has a slope of \( 34 \)), I should clarify how to select one of the provided options.

If you must choose one of the four lines despite them not being parallel to \( y = 34x - 2 \), I would suggest choosing one based on either the least deviation from the slope or some other criteria.

However, if the task is strictly to identify which one is "closest," we may focus on the ones with the highest slope values from the options. Both \( 4x - 3y = 12 \) and \( 4x - 3y = 6 \) yield a slope of \( \frac{4}{3} \), which while far from \( 34 \), is still greater than \( \frac{3}{4} \).

Thus, if you need to select one option as the best (though it is not parallel), you might choose:

4x - 3y = 12 or 4x - 3y = 6

(both of which give the slope \( \frac{4}{3} \)). You could choose either one based on your preference, as both are equivalent in terms of slope.

only one

Understood! Given that I must choose only one line from your options, I will select:

\( 4x - 3y = 12 \)

This is one of the lines with the highest slope from the choices provided. Thank you for your patience!

Which line is parallel to the line y=56x and goes through the point (12,6)?(1 point)
Responses

6y=5x
6 y equals 5 x

y=56x+6
y equals Start Fraction 5 over 6 End Fraction x plus 6

y=56x−4
y equals Start Fraction 5 over 6 End Fraction x minus 4

y=−65x+6

To determine which line is parallel to the line \( y = 56x \) and goes through the point \( (12, 6) \), we need to find a line that has the same slope as \( y = 56x \) and passes through that point.

  1. Finding the slope:

    • The slope of the line \( y = 56x \) is \( 56 \).

  2. Using the point-slope form: A line that passes through the point \( (x_1, y_1) = (12, 6) \) with a slope of \( m = 56 \) can be expressed in point-slope form as: \[ y - y_1 = m(x - x_1) \] Plugging in \( 6 \) for \( y_1 \), \( 56 \) for \( m \), and \( 12 \) for \( x_1 \): \[ y - 6 = 56(x - 12) \ y - 6 = 56x - 672 \ y = 56x - 666 \]

  3. Now, we must analyze the options: Let's convert the options into the slope-intercept form to check if they have the same slope of \( 56 \).

  • Option 1: \( 6y = 5x \) \[ y = \frac{5}{6}x \quad \text{(slope is } \frac{5}{6} \text{)} \]

  • Option 2: \( y = 56x + 6 \) \[ \text{(slope is } 56 \text{; does not pass through } (12,6) \text{)} \]

  • Option 3: \( y = 56x - 4 \) \[ \text{(slope is } 56 \text{; does not pass through } (12,6) \text{)} \]

  • Option 4: \( y = -65x + 6 \) \[ \text{(slope is } -65 \text{)} \]

Conclusion: The lines with the same slope of \( 56 \) are Option 2 and Option 3.

Since neither passes through \( (12, 6) \), we can't find a valid answer. However, if the goal is only to find parallel lines, both options (2 and 3) are technically parallel to \( y = 56x \), but they do not meet the point criteria.

If the question strictly requires a choice from the options based on parallelism, Option 2: \( y = 56x + 6 \) is the most appropriate response since it maintains the same slope.

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 negative 3 x plus 9

y=−13x+9
y equals negative Start Fraction 1 over 3 End Fraction x plus 9

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

y=13x+9

To find an equation of a line that is perpendicular to the line \( y = -3x + 5 \), we first need to determine its slope and then find the negative reciprocal of that slope.

  1. Identify the slope of the given line:

    • The slope (\( m \)) of the line \( y = -3x + 5 \) is \( -3 \).

  2. Find the negative reciprocal of the slope:

    • The negative reciprocal of \( -3 \) is: \[ \frac{1}{3} \]

  3. Using the new slope: A line that is perpendicular to the given line will have a slope of \( \frac{1}{3} \).

Now, let's evaluate the provided options to find one that has a slope of \( \frac{1}{3} \).

  • Option 1: \( y = -3x + 9 \)

    • Slope: \( -3 \) (not perpendicular)

  • Option 2: \( y = -\frac{1}{3}x + 9 \)

    • Slope: \( -\frac{1}{3} \) (not perpendicular)

  • Option 3: \( y = 3x + 9 \)

    • Slope: \( 3 \) (not perpendicular)

  • Option 4: \( y = 13x + 9 \)

    • Slope: \( 13 \) (not perpendicular)

None of these options contain a slope of \( \frac{1}{3} \), but it looks like I misinterpreted Option 2. It has a slope of \( -\frac{1}{3} \) which is also incorrect.

Checking:

  • Perpendicular slope should be: \( \frac{1}{3} \).

Since none of the options have the correct slope of \( \frac{1}{3} \), it appears that there might not be a suitable answer provided in the responses to indicate a line that is perpendicular to \( y = -3x + 5 \).

However, based on the context, the option that has the nearest slope in terms of a normal positive slope would mean:

Choose Option 3: \( y = 3x + 9 \) as it has the possibility of being a parallel line.

If you require one exclusively based on perpendicularity from the options given, it appears none fit that requirement.