Linear equations in two variables
- Course
- Algebra
- Question type
- Linear equations in two variables
- Practice
- 6 practice questions
- Language
- Vietnamese · English
About this lesson
Linear equations in two variables, Ax + By = C: reading the slope and both intercepts, writing the equation of a line through two points, building an equation from a word problem, and interpreting each coefficient in context.
On the Digital SAT, linear equations in two variables belong to the Algebra domain and are among the most frequent math questions. You may get an equation in standard form and be asked for its slope or an intercept, two points and a request for the line through them, or a story about two items with different prices followed by "which equation represents this situation" or "what does this coefficient mean".
Most mistakes happen while reading, not while calculating: using A/B instead of −A/B, swapping the x- and y-intercepts, or attaching a price to the wrong variable. This lesson gives three quick readings of Ax + By = C, a reliable way to write a line from two points, a simple rule for interpreting coefficients in context, and point-testing and Desmos checks for the answer choices. It ends with 6 self-graded practice questions, each with a full explanation.
What you'll learn
- Switch between Ax + By = C and y = mx + b without flipping the slope's sign.
- Read the slope and both intercepts directly from an equation.
- Write the equation of a line through two points, or parallel or perpendicular to another line.
- Turn a word problem into an equation and explain what each coefficient means.
Lesson contents
- Lesson goals
- 1. The forms of a line
- Key terms
- Reading Ax + By = C quickly
- 2. Writing the equation of a line
- Through two points
- Parallel and perpendicular
- 3. Word problems: two quantities, one total
- 4. Common traps
- 5. Speed strategies
This lesson is part of HOCSAT Learn
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