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 or negative).

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.

Front

What is the graph of y = -¼x + 3?

Back

The graph of y = -¼x + 3 has a slope of -¼ and a y-intercept of 3. It decreases as x increases.

Front

How do you find the slope from the equation y = (1/2)x?

Back

The slope from the equation y = (1/2)x is 1/2, indicating that for every 2 units you move right, you move up 1 unit.

Front

What does the equation y = ⅖x + 2 represent?

Back

The equation y = ⅖x + 2 represents a line with a slope of ⅖ and a y-intercept of 2.

Front

How do you graph the equation y = ⅔x - 1?

Back

To graph y = ⅔x - 1, start at the y-intercept (0, -1) and use the slope of ⅔ to rise 2 units up and run 3 units to the right.

Front

What is the significance of the solution pairs in a linear graph?

Back

The solution pairs in a linear graph represent all the (x, y) coordinates that satisfy the linear equation.

Front

What is the general form of a linear equation?

Back

The general form of a linear equation is Ax + By = C, where A, B, and C are constants.