Writing Equations of Parallel and Perpendicular Lines
Master Writing Equations of Parallel and Perpendicular Lines in Grade 10 math. To write the equation of a line, first determine its slope ()
Key Concepts
To write the equation of a line, first determine its slope ($m$). For a parallel line, use the same slope. For a perpendicular line, use the negative reciprocal slope. Then, use the point slope formula with a known point $(x 1, y 1)$. $$y y 1 = m(x x 1)$$.
Find the line parallel to $y = 3x + 1$ through $(2, 4)$. The slope is $m=3$. Equation: $y 4 = 3(x 2)$, which simplifies to $y = 3x 2$. Find the line perpendicular to $y = 2x + 5$ through $(4, 0)$. The new slope is $m=\frac{1}{2}$. Equation: $y 0 = \frac{1}{2}(x 4)$, which simplifies to $y = \frac{1}{2}x 2$.
Want to create a line that's a perfect partner to an existing one? First, find its slope—either the same for a parallel pal or the opposite reciprocal for a perpendicular rival. Then, grab the one point you know the new line passes through and plug it all into the point slope formula to reveal the line's full equation!
Common Questions
What is Writing Equations of Parallel and Perpendicular Lines in Grade 10 math?
To write the equation of a line, first determine its slope ().
How do you apply Writing Equations of Parallel and Perpendicular Lines?
Find the line parallel to through The slope is.
Why is Writing Equations of Parallel and Perpendicular Lines important for students?
Want to create a line that's a perfect partner to an existing one? First, find its slope—either the same for a parallel pal or the opposite reciprocal for a perpendicular rival.