Algebra 1 review flashcard 2

Front

What does it mean if an equation has infinite solutions?

Back

An equation has infinite solutions when any value of the variable satisfies the equation, meaning the two sides of the equation are equivalent for all values.

Front

How do you determine the slope of a line from its equation?

Back

The slope of a line can be determined from the equation in the form y = mx + b, where m is the slope.

Front

What is the y-intercept of a linear equation?

Back

The y-intercept is the point where the line crosses the y-axis, represented as (0, b) in the equation y = mx + b.

Front

How do you simplify the equation 3x - 7 = 3(x - 3) + 2?

Back

Distributing gives 3x - 7 = 3x - 9 + 2, which simplifies to 3x - 7 = 3x - 7, indicating infinite solutions.

Front

What is the general form of a quadratic equation?

Back

The general form of a quadratic equation is ax² + bx + c = 0, where a, b, and c are constants.

Front

How do you find the number of solutions from a graph?

Back

The number of solutions corresponds to the number of points where the graph intersects the x-axis.

Front

What is the formula for finding the slope between two points (x1, y1) and (x2, y2)?

Back

The slope (m) is calculated as m = (y2 - y1) / (x2 - x1).

Front

What does it mean if a linear equation has no solutions?

Back

A linear equation has no solutions when the lines are parallel and never intersect.

Front

How do you convert (x + 5)(x + 4) into general form?

Back

Expanding gives x² + 4x + 5x + 20 = x² + 9x + 20.

Front

What is the significance of the slope in a linear equation?

Back

The slope indicates the steepness and direction of the line; a positive slope rises, while a negative slope falls.