Example Card: Writing Equations of Parallel Lines
Practice writing equations of parallel lines in Grade 9 math — Let's use one line as a blueprint to build another that runs perfectly alongside it.
Key Concepts
Let's use one line as a blueprint to build another that runs perfectly alongside it. This example tackles the first key idea: writing equations for parallel lines.
Example Problem Write an equation in slope intercept form for the line that passes through ( 3, 5) and is parallel to a line with equation $y = 3x + 2$.
Step by Step 1. First, determine the slope of the given line. The equation $y = 3x + 2$ is in slope intercept form, so its slope is $3$. Any line parallel to it must have the same slope. 2. Now we have the slope $m = 3$ and a point ( 3, 5). We can use the point slope formula to find the new line's equation. $$ y y 1 = m(x x 1) $$ 3. Substitute the slope and the coordinates of the point into the formula. $$ y 5 = 3(x ( 3)) $$ 4. Simplify the expression inside the parentheses. $$ y 5 = 3(x + 3) $$ 5. Apply the Distributive Property to the right side of the equation. $$ y 5 = 3x + 9 $$ 6. To get the final equation in slope intercept form, isolate $y$ by adding $5$ to both sides. $$ y = 3x + 14 $$.
Common Questions
What is 'Writing Equations of Parallel Lines' in Grade 9 math?
Let's use one line as a blueprint to build another that runs perfectly alongside it. This example tackles the first key idea: writing equations for parallel lines.
How do you solve problems involving 'Writing Equations of Parallel Lines'?
This example tackles the first key idea: writing equations for parallel lines. First, determine the slope of the given line.
Why is 'Writing Equations of Parallel Lines' an important Grade 9 math skill?
For an equation like $6x + 3y = 9$, the slope is NOT 6.. You must solve for $y$ first to put the equation in $y = mx + b$ form before you can correctly identify the slope.