If two lines are parallel and one line has the equation y = 5x + 1, what is the
Practice Questions
Q1
If two lines are parallel and one line has the equation y = 5x + 1, what is the equation of a line parallel to it that passes through the point (2, 3)?
y = 5x - 7
y = 5x + 7
y = 5x + 1
y = 5x - 1
Questions & Step-by-Step Solutions
If two lines are parallel and one line has the equation y = 5x + 1, what is the equation of a line parallel to it that passes through the point (2, 3)?
Step 1: Identify the slope of the given line. The equation is y = 5x + 1, so the slope (m) is 5.
Step 2: Since parallel lines have the same slope, the slope of the new line will also be 5.
Step 3: Use the point-slope form of a line, which is y - y1 = m(x - x1), where (x1, y1) is a point on the line. Here, (x1, y1) is (2, 3).
Step 4: Substitute the slope and the point into the point-slope form: y - 3 = 5(x - 2).
Step 5: Simplify the equation. Distribute the 5: y - 3 = 5x - 10.
Step 6: Add 3 to both sides to solve for y: y = 5x - 10 + 3.
Step 7: Combine like terms: y = 5x - 7.
Step 8: The final equation of the line parallel to y = 5x + 1 that passes through (2, 3) is y = 5x - 7.
