Question

Parallel & Perpendicular Lines Quick Check
2 of 52 of 5 Items
Question
Which line is parallel to the line y=56x
and goes through the point (12,6)
?(1 point)
Responses

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

6y=5x
6 y equals 5 x

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

y=−6/5x+6

Answer 1

To find the line that is parallel to the line \( y = \frac{5}{6}x \) and goes through the point (12,6), we need to know that parallel lines have the same slope.

The slope of the given line \( y = \frac{5}{6}x \) is \( \frac{5}{6} \). Therefore, any parallel line will also have this slope.

Now, we can use the point-slope form of a linear equation, which 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. Here, \( m = \frac{5}{6} \) and \((x_1, y_1) = (12, 6)\).

Using the point-slope form:

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

Solving for \( y \):

\[
y - 6 = \frac{5}{6}x - \frac{5}{6} \cdot 12
\]
\[
y - 6 = \frac{5}{6}x - 10
\]
\[
y = \frac{5}{6}x - 10 + 6
\]
\[
y = \frac{5}{6}x - 4
\]

So the equation of the line parallel to \( y = \frac{5}{6}x \) that goes through the point (12,6) is \( y = \frac{5}{6}x - 4 \).

Thus, the correct response is:

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