Core Algebra 1 concepts: solving linear equations, slope-intercept form, and systems of equations, explained conceptually.
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- What is a linear equation?
- An equation in which the variable has an exponent of 1 and the graph is a straight line.
- What is the standard form of a linear equation?
- Ax + B = C, where A, B, and C are constants and x is the variable.
- What does the addition property of equality state?
- If you add the same number to both sides of an equation, the equation remains true.
- What does the multiplication property of equality state?
- If you multiply both sides of an equation by the same nonzero number, the equation remains true.
- How do you solve a multi-step equation?
- Use inverse operations in reverse order: undo addition or subtraction first, then multiplication or division.
- When you have variables on both sides of an equation, what is the first step?
- Move all variable terms to one side using addition or subtraction.
- How does the distributive property apply when solving equations?
- Multiply the term outside the parentheses by each term inside: a(b + c) = ab + ac.
- What does it mean to combine like terms in an equation?
- Add or subtract terms that have the same variable raised to the same power.
- How do you check if your solution to an equation is correct?
- Substitute the solution back into the original equation to see if both sides are equal.
- What does it mean when a linear equation has no solution?
- The variable cancels out and you are left with a false statement, like 0 = 5.
- What does it mean when a linear equation has infinite solutions?
- The variable cancels out and you are left with a true statement, like 0 = 0, meaning every number works.
- How do you solve an equation with fractions?
- Multiply every term by the least common denominator to clear the fractions, then solve.
- What is slope-intercept form?
- y = mx + b, where m is the slope and b is the y-intercept.
- What is slope?
- The measure of how steep a line is, calculated as the ratio of vertical change to horizontal change (rise over run).
- What is the y-intercept?
- The point where a line crosses the y-axis, where x = 0.