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 y=2/5x+ ____

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 can follow these steps:

1. **Identify the slope of the given line**: The slope of the line \( y = \frac{2}{5}x + 1 \) is \( \frac{2}{5} \).

2. **Use the slope-point form of the line equation**: The slope-point 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. Here, \( m = \frac{2}{5} \) and the point is \( (5, 5) \).

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

4. **Distribute on the right side**:
\[
y - 5 = \frac{2}{5}x - \frac{10}{5}
\]
\[
y - 5 = \frac{2}{5}x - 2
\]

5. **Add 5 to both sides**:
\[
y = \frac{2}{5}x - 2 + 5
\]
\[
y = \frac{2}{5}x + 3
\]

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

\[
\boxed{y = \frac{2}{5}x + 3}
\]