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+
.
Remaining Att

Answer 1

To find the equation of a line that is parallel to the line \( y = 25x + 1 \), we first note that parallel lines have the same slope. The slope of the given line is 25.

Now, we use the point-slope form of the equation of a line, 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. In this case, \( m = 25 \) and \( (x_1, y_1) = (5, 5) \).

Plugging these values into the point-slope equation:

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

Now, 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:

\[
y = 25x - 120
\]

So in the format requested:

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