Flashcard - Writing Linear Equations, Word Problems, Inequalities

Front

What is a linear equation?

Back

A linear equation is an equation that represents a straight line when graphed. It can be written in the form y = mx + b, where m is the slope and b is the y-intercept.

Front

What does the slope of a line represent?

Back

The slope of a line represents the rate of change of y with respect to x. It indicates how steep the line is and the direction it goes (positive or negative).

Front

How do you determine if a point is part of the solution set of a linear equation?

Back

To determine if a point is part of the solution set, substitute the x and y values of the point into the equation. If the equation holds true, the point is part of the solution set.

Front

What is the y-intercept of a linear equation?

Back

The y-intercept is the point where the line crosses the y-axis. It is represented by the value of b in the equation y = mx + b.

Front

How can you write the equation of a line given two points?

Back

To write the equation of a line given two points, first calculate the slope (m) using the formula m = (y2 - y1) / (x2 - x1). Then use the point-slope form y - y1 = m(x - x1) to find the equation.

Front

What is the difference between a linear equation and a linear inequality?

Back

A linear equation represents a straight line, while a linear inequality represents a region of the graph that is above or below the line, indicating a range of possible solutions.

Front

How do you graph a linear inequality?

Back

To graph a linear inequality, first graph the corresponding linear equation as a dashed or solid line (depending on whether the inequality is strict or inclusive). Then shade the region that satisfies the inequality.

Front

What does the term 'solution set' refer to in the context of linear equations?

Back

The solution set refers to all the points (x, y) that satisfy the linear equation. It is the set of all possible solutions.

Front

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

Back

The coefficients in a linear equation determine the slope and the y-intercept of the line. They affect the steepness and position of the line on the graph.

Front

How can you interpret the meaning of a linear equation in a real-world context?

Back

A linear equation can represent relationships between quantities in real-world scenarios, such as cost, distance, or population growth, where one quantity changes at a constant rate relative to another.