Linear Equations Review

Front

What is a linear equation?

Back

A linear equation is an equation that makes 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 (upward or downward).

Front

How do you calculate the slope between two points (x1, y1) and (x2, y2)?

Back

The slope (m) is calculated using the formula m = (y2 - y1) / (x2 - x1).

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

If a line has a slope of 0, what does that mean?

Back

A slope of 0 means the line is horizontal, indicating that there is no change in y as x changes.

Front

What does a negative slope indicate about a line?

Back

A negative slope indicates that the line is decreasing, meaning as x increases, y decreases.

Front

What is the constant rate of change in a linear relationship?

Back

The constant rate of change is the same as the slope of the line. It shows how much y changes for a unit change in x.

Front

How can you determine if a point lies on a line represented by a linear equation?

Back

To determine if a point (x, y) lies on the line, substitute x into the equation and see if the resulting y value matches the y-coordinate of the point.

Front

What is the significance of the coordinates in a point on a line?

Back

The coordinates (x, y) represent a specific location on the line, where x is the input value and y is the output value.

Front

How do you interpret the equation y = 0.30x in a real-world context?

Back

This equation indicates that for every cookie purchased (x), the cost (y) increases by $0.30.