Algebra / Linear Equations Two Variables
Linear Equations, Intercepts, and Points
Two-variable linear equations can be interpreted through intercepts, points on a graph, and context equations with two quantities.
Least you need to know
- To find the $x$-intercept, set $y=0$.
- To find the $y$-intercept, set $x=0$.
- A point lies on a graph if its coordinates make the equation true.
Key notation
- $3x+4y=24$ — A linear equation whose intercepts can be found by setting one variable to 0
Worked example
- For $2x+5y=20$, the $x$-intercept occurs when $y=0$.
- Then $2x=20$, so $x=10$.
Common mistakes
- Intercept questions ask for a coordinate or a coordinate value.
- Substitute both coordinates when checking whether a point lies on a graph.
How to recognize it
- The problem asks about an intercept.
- The problem gives a point and asks for a parameter.
- The equation contains both $x$ and $y$.
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