Question

Write the equation that is parallel to the graph given, and goes through (6,8)



a
y=2x+8

b
y=2x-8

c
y=(1/2)x-3

Answer 1

To find the equation of a line that is parallel to a given line and goes through a specific point, we need to know the slope of the given line, as parallel lines have the same slope.

The equation provided is \( y = 2x + 8 \). The slope (m) of this line is 2.

Now we need to write the equation of a line with the same slope (2) that passes through the point (6, 8). We can use the point-slope form of the equation of a line, which is:

\[
y - y_1 = m(x - x_1)
\]

Here, \( (x_1, y_1) = (6, 8) \) and \( m = 2 \):

\[
y - 8 = 2(x - 6)
\]

Now, we can simplify this equation:

\[
y - 8 = 2x - 12
\]

Adding 8 to both sides:

\[
y = 2x - 4
\]

Now we can compare this with the options given:

a. \( y = 2x + 8 \)
b. \( y = 2x - 8 \)
c. \( y = \frac{1}{2}x - 3 \)

None of the provided options match the correct equation \( y = 2x - 4 \).

It seems that a correct answer is not listed among the options.