Graphing a Direct Variation
Solve graphing a direct variation in Grade 9 math — Explanation Graphing a direct variation is a piece of cake! Part of Polynomials and Factoring for Grade 9.
Key Concepts
Property The graph of a direct variation equation, $y=kx$, is always a straight line that must pass through the origin $(0, 0)$.
Explanation Graphing a direct variation is a piece of cake! You already know the first point is always the origin, $(0,0)$. All you need is one other point from the relationship. Plot that second point, grab a ruler, and draw a straight line connecting it to the origin. Voila! Your graph is complete and represents every possible point.
Examples To graph $y=3x$, start at $(0,0)$. Find another point, such as $(2,6)$, and draw a line through both. A machine makes 5 gadgets for 10 dollars. To graph this, plot the origin $(0,0)$ and the point $(5,10)$. The line shows the cost for any number of gadgets.
Common Questions
What is 'Graphing a Direct Variation' in Grade 9 math?
Explanation Graphing a direct variation is a piece of cake! You already know the first point is always the origin, $(0,0)$.
How do you solve problems involving 'Graphing a Direct Variation'?
You already know the first point is always the origin, $(0,0)$. All you need is one other point from the relationship.
Why is 'Graphing a Direct Variation' an important Grade 9 math skill?
Write the final equation by putting the value of $k$ back into the formula: $$d = 60t$$ Common mistake tip: A common slip-up is calculating $k$ upside down by doing $k = \frac{x}{y}$.. Always remember to find the constant, you divide the output variable (y) by the input variable (x).