Writing Equations of Parallel Lines
Write equations of parallel lines in Grade 9 algebra. Use the same slope as the given line with point-slope form to create parallel line equations through specified points.
Key Concepts
Property To write an equation for a line that passes through a point $(x 1, y 1)$ and is parallel to a given line, use the same slope $(m)$ from the given line and substitute it into the point slope formula: $y y 1 = m(x x 1)$. Explanation Imagine you're laying down a new train track that must run parallel to an old one but has to pass through a specific town. You already know the direction to go—just copy the slope from the old track! Then, use the town's location (the point) to pin your new track in the exact right place using the point slope formula. Examples To find a line through $(2, 5)$ parallel to $y = 3x + 1$: use slope $m=3$. The equation is $y 5 = 3(x 2)$, which simplifies to $y = 3x 1$. To find a line through $( 4, 1)$ parallel to $y = \frac{1}{2}x 7$: use slope $m = \frac{1}{2}$. The equation is $y 1 = \frac{1}{2}(x ( 4))$, which simplifies to $y = \frac{1}{2}x 1$.
Common Questions
How do you write the equation of a line parallel to a given line?
Parallel lines have equal slopes. Find the slope of the given line, then use point-slope form y - y₁ = m(x - x₁) with the new point and that same slope.
What is the relationship between slopes of parallel lines?
Parallel lines have identical slopes but different y-intercepts. If the original line has slope m, any parallel line also has slope m — they rise at the same rate without meeting.
How do you find slope from standard form Ax + By = C?
Solve for y to get slope-intercept form: y = -(A/B)x + (C/B). The coefficient of x is the slope m.