Which line is parallel to the line y=5/6x and goes through the point (12,6)?(1 point)

Question

Responses

6y=5x
6 y equals 5 x

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

y=−65x+6
y equals negative Start Fraction 6 over 5 End Fraction x plus 6

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

Answer 1

To find a line that is parallel to the line given by the equation \( y = \frac{5}{6}x \) and also passes through the point \( (12, 6) \), we need to maintain the same slope, which is \( \frac{5}{6} \).

1. Since the slope of the new line will also be \( \frac{5}{6} \), we can use the point-slope form of a line, which is \( y - y_1 = m(x - x_1) \), where \( (x_1, y_1) \) is the point the line goes through, and \( m \) is the slope.

2. Plugging in the point \( (12, 6) \) and the slope \( \frac{5}{6} \):

   \[ y - 6 = \frac{5}{6}(x - 12) \]

3. Distributing the slope:

   \[ y - 6 = \frac{5}{6}x - 10 \]

4. Adding 6 to both sides:

   \[ y = \frac{5}{6}x - 4 \]

Now let's look at the given responses:

• \( 6y = 5x \)
• \( y = \frac{5}{6}x + 6 \)
• \( y = -\frac{6}{5}x + 6 \)
• \( y = \frac{5}{6}x - 4 \)

The equation we derived, \( y = \frac{5}{6}x - 4 \), matches exactly with the fourth option.

Thus, the correct response is:

\( y = \frac{5}{6}x - 4 \).