FA7-2: Graphing Linear Equations

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 (m) represent in a linear equation?

Back

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

Front

What is the y-intercept (b) in a linear equation?

Back

The y-intercept (b) is the point where the line crosses the y-axis. It is the value of y when x is 0.

Front

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

Back

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

Front

What does it mean for a line to have a positive slope?

Back

A line with a positive slope rises from left to right, indicating that as x increases, y also increases.

Front

What does it mean for a line to have a negative slope?

Back

A line with a negative slope falls from left to right, indicating that as x increases, y decreases.

Front

What is the standard form of a linear equation?

Back

The standard form of a linear equation is Ax + By = C, where A, B, and C are integers, and A should be non-negative.

Front

How can you graph a linear equation using the slope and y-intercept?

Back

To graph a linear equation, start at the y-intercept (0, b) on the y-axis, then use the slope (rise/run) to find another point on the line.

Front

What is the significance of the point (0, b) in a linear equation?

Back

The point (0, b) is the y-intercept, which shows where the line crosses the y-axis.

Front

How do 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 equals the y-coordinate of the point.