Question

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

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
y equals negative Start Fraction 6 over 5 End Fraction x plus 6

6y=5x

Answer 1

To find a line that is parallel to the line \( y = \frac{5}{6}x \) and goes through the point \( (12, 6) \), we can follow these steps:

1. **Identify the slope of the given line:** The slope of the line \( y = \frac{5}{6}x \) is \( \frac{5}{6} \).

2. **Use the point-slope form of a line:** Since parallel lines have the same slope, the equation of the line we are looking for will also have a slope of \( \frac{5}{6} \).
The point-slope form of a line is:
\[
y - y_1 = m(x - x_1)
\]
where \( m \) is the slope, and \( (x_1, y_1) \) is the point through which the line passes.

3. **Substituting the values:**
Here, \( m = \frac{5}{6} \) and \( (x_1, y_1) = (12, 6) \):
\[
y - 6 = \frac{5}{6}(x - 12)
\]

4. **Simplify the equation:**
\[
y - 6 = \frac{5}{6}x - \frac{5}{6} \times 12
\]
\[
y - 6 = \frac{5}{6}x - 10
\]
\[
y = \frac{5}{6}x - 10 + 6
\]
\[
y = \frac{5}{6}x - 4
\]

Thus, the equation of the line parallel to \( y = \frac{5}{6}x \) and passing through the point \( (12, 6) \) is:
\[
y = \frac{5}{6}x - 4
\]

This matches the second response option from your list. Therefore, the answer is:

**y equals Start Fraction 5 over 6 End Fraction x minus 4.**