Question

Find the equation of the line parallel to.
y, equals, 5, x, minus, 3, .y=5x−3
and going through the point. , left parenthesis, 1, comma, 7, right parenthesis, .
(1,7)

your answer should be in slope intercept form. , y, equals, m, x, plus, b
y=mx+b

Answer 1

To find the equation of a line that is parallel to the line given by \( y = 5x - 3 \) and passes through the point \( (1, 7) \), we can follow these steps:

1. **Identify the slope of the given line**: The slope-intercept form of the line is \( y = mx + b \), where \( m \) is the slope. For the line \( y = 5x - 3 \), the slope \( m \) is \( 5 \).

2. **Use the same slope for the parallel line**: Since parallel lines have the same slope, the slope of our line will also be \( 5 \).

3. **Use the point-slope form to find the equation**: We can use the point-slope form of a line equation:
\[
y - y_1 = m(x - x_1)
\]
where \( (x_1, y_1) \) is the point we know, \( (1, 7) \), and \( m = 5 \):
\[
y - 7 = 5(x - 1)
\]

4. **Simplify to get the slope-intercept form**:
\[
y - 7 = 5x - 5
\]
\[
y = 5x - 5 + 7
\]
\[
y = 5x + 2
\]

Therefore, the equation of the line parallel to \( y = 5x - 3 \) and passing through the point \( (1, 7) \) is:

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