Question

Find the equation of the line that is parallel to the line y=25x+1
and passes through the point (5,5)
.(1 point)
The line that is parallel to y=25x+1
and passes through the point (5,5)
is y=25x+

Answer 1

To find the equation of a line that is parallel to the line \( y = 25x + 1 \) and passes through the point \( (5, 5) \), we start by noting that parallel lines have the same slope.

The slope of the given line \( y = 25x + 1 \) is \( 25 \).

Since we want the new line to pass through the point \( (5, 5) \) and have the same slope, we can use the point-slope form of the equation of a line, which is given by:

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

Where \( m \) is the slope, and \( (x_1, y_1) \) is the point the line passes through.

Substituting \( m = 25 \), \( x_1 = 5 \), and \( y_1 = 5 \) into the formula, we get:

\[
y - 5 = 25(x - 5)
\]

Now, we distribute on the right side:

\[
y - 5 = 25x - 125
\]

Next, we add \( 5 \) to both sides to solve for \( y \):

\[
y = 25x - 120
\]

Thus, the equation of the line that is parallel to \( y = 25x + 1 \) and passes through the point \( (5,5) \) is:

\[
y = 25x - 120
\]

Which can be filled in the blank as:

The line that is parallel to \( y = 25x + 1 \) and passes through the point \( (5,5) \) is \( y = 25x - 120 \).