Question

Which line is parallel to the line y=56x−4
and goes through the point (0, 6)
?(1 point)
Responses

6x=5y
6 x is equal to 5 y

y=56x−4
y is equal to 5 sixths x minus 4

y=56x+6
y is equal to 5 sixths x plus 6

y=−65x+6

Answer 1

To find a line that is parallel to the line \( y = \frac{5}{6}x - 4 \) and passes through the point \( (0, 6) \), we need to identify that parallel lines have the same slope.

The slope of the given line \( y = \frac{5}{6}x - 4 \) is \( \frac{5}{6} \).

Now, we can use the point-slope form of the line to write the equation of the parallel line that goes through the point \( (0, 6) \):

1. Start with the point-slope form:
\[
y - y_1 = m(x - x_1)
\]
where \( m \) is the slope and \( (x_1, y_1) \) is the point through which the line passes.

2. Substitute \( m = \frac{5}{6} \), \( x_1 = 0 \), and \( y_1 = 6 \):
\[
y - 6 = \frac{5}{6}(x - 0)
\]
\[
y - 6 = \frac{5}{6}x
\]
\[
y = \frac{5}{6}x + 6
\]

So the equation of the line parallel to \( y = \frac{5}{6}x - 4 \) and passing through \( (0, 6) \) is

\[
y = \frac{5}{6}x + 6.
\]

Thus, the correct response is:

**y = \frac{5}{6}x + 6** (which corresponds with the option **y=56x+6**, likely a formatting error).