Question

Find the equation of the line that is parallel to the line y=2/5x+1
and passes through the point (5,5)
.(1 point)
The line that is parallel to y=2/5x+1
and passes through the point (5,5)
is

Answer 1

To find the equation of a line that is parallel to the line \( y = \frac{2}{5}x + 1 \) and passes through the point \( (5, 5) \), we follow these steps:

1. **Identify the slope of the original line**: The slope of the line \( y = \frac{2}{5}x + 1 \) is \( \frac{2}{5} \). Since parallel lines have the same slope, the slope of the new line will also be \( \frac{2}{5} \).

2. **Use the point-slope form of a line**: The point-slope form of a line is given by:
\[
y - y_1 = m(x - x_1)
\]
where \( m \) is the slope and \( (x_1, y_1) \) is a point on the line. In this case, \( m = \frac{2}{5} \) and the point is \( (5, 5) \).

3. **Plug in the values**:
\[
y - 5 = \frac{2}{5}(x - 5)
\]

4. **Simplify the equation**:
Distributing the slope on the right side gives:
\[
y - 5 = \frac{2}{5}x - \frac{2}{5} \cdot 5
\]
\[
y - 5 = \frac{2}{5}x - 2
\]
Now, add 5 to both sides:
\[
y = \frac{2}{5}x - 2 + 5
\]
\[
y = \frac{2}{5}x + 3
\]

So, the equation of the line that is parallel to \( y = \frac{2}{5}x + 1 \) and passes through the point \( (5, 5) \) is:
\[
\boxed{y = \frac{2}{5}x + 3}
\]