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 = 0.

Front

How do you graph the equation y = x - 2?

Back

To graph y = x - 2, start at the y-intercept (0, -2) and use the slope of 1 to rise 1 unit up and run 1 unit to the right to find another point.

Front

What is the graph of y = (1/2)x?

Back

The graph of y = (1/2)x is a straight line that passes through the origin (0,0) with a slope of 1/2, meaning it rises 1 unit for every 2 units it runs.

Front

How do you graph the equation y = 3x - 4?

Back

To graph y = 3x - 4, start at the y-intercept (0, -4) and use the slope of 3 to rise 3 units up and run 1 unit to the right.

Front

What does the equation y = ⅔x - 1 represent?

Back

The equation y = ⅔x - 1 represents a line with a slope of ⅔ and a y-intercept of -1.

Front

How do you graph the equation x = 2?

Back

The equation x = 2 is a vertical line that crosses the x-axis at the point (2,0). All points on this line have an x-coordinate of 2.

Front

What is the difference between a positive slope and a negative slope?

Back

A positive slope means the line rises from left to right, while a negative slope means the line falls from left to right.

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.