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 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

What is the y-intercept?

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 do you graph the equation y = 2x + 3?

Back

To graph y = 2x + 3, start at the y-intercept (0, 3) on the y-axis. From there, use the slope (2) to rise 2 units up and run 1 unit to the right to find another point.

Front

What does the equation x = 1 represent on a graph?

Back

The equation x = 1 represents a vertical line that crosses the x-axis at the point (1, 0).

Front

What does the equation y = -4 represent on a graph?

Back

The equation y = -4 represents a horizontal line that crosses the y-axis at the point (0, -4).

Front

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

Back

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

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

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 does it mean if two lines are parallel?

Back

Two lines are parallel if they have the same slope but different y-intercepts, meaning they will never intersect.