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 need to use the fact that parallel lines have the same slope.

The slope of the given line \(y = 25x + 1\) is \(25\). Therefore, the line we are looking for will also have a slope of \(25\).

Using the point-slope form of a linear equation, which is given by:

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

where \(m\) is the slope and \((x_1, y_1)\) is the point through which the line passes, we can substitute \(m = 25\), \(x_1 = 5\), and \(y_1 = 5\):

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

Now, we can simplify this equation:

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

Adding \(5\) to both sides gives:

\[
y = 25x - 120
\]

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

\[
\boxed{y = 25x - 120}
\]