Writing an Equation Given a Point
Apply writing an equation given a point in Grade 9 math — Then, use that $k$ to write the final equation. Part of Polynomials and Factoring for Grade 9.
Key Concepts
Property To write a direct variation equation, first find the constant of variation, $k$, by substituting the coordinates of a given point into $y = kx$. Then, use that $k$ to write the final equation.
Explanation If you know just one point on a direct variation line, you hold the secret key! Just plug the x and y values from that point into the formula $y = kx$. This allows you to solve for 'k,' the magic multiplier. Once you have k, you can write the full equation that defines the entire relationship.
Examples For a direct variation including $(5, 30)$: Substitute into $y=kx \rightarrow 30 = k \cdot 5 \rightarrow k=6$. The equation is $y=6x$. For a direct variation including $(8, 4)$: Substitute into $y=kx \rightarrow 4 = k \cdot 8 \rightarrow k= \frac{4}{8}= \frac{1}{2}$. The equation is $y= \frac{1}{2}x$.
Common Questions
What is 'Writing an Equation Given a Point' in Grade 9 math?
Then, use that $k$ to write the final equation. Explanation If you know just one point on a direct variation line, you hold the secret key!.
How do you solve problems involving 'Writing an Equation Given a Point'?
Explanation If you know just one point on a direct variation line, you hold the secret key! Just plug the x and y values from that point into the formula $y = kx$.
Why is 'Writing an Equation Given a Point' an important Grade 9 math skill?
Always remember that the value of $k$ is found by dividing $y$ by $x$.. To keep it straight, think of the phrase "Y to the sky" to remember that $y$ goes in the numerator (on top).