Graphing Linear Equations

Front

What is a linear equation?

Back

An equation that makes a straight line when graphed, typically in the form y = mx + b.

Front

What does the 'm' in the equation y = mx + b represent?

Back

The slope of the line, indicating the rate of change of y with respect to x.

Front

What does the 'b' in the equation y = mx + b represent?

Back

The y-intercept, which is the point where the line crosses the y-axis.

Front

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

Back

Slope (m) = (y2 - y1) / (x2 - x1).

Front

What is the y-intercept of the equation y = 2x + 5?

Back

5, because it is the value of y when x = 0.

Front

What is the x-intercept of the equation y = -3x + 6?

Back

2, because it is the value of x when y = 0.

Front

How do you graph a linear equation?

Back

1. Identify the slope (m) and y-intercept (b). 2. Plot the y-intercept on the graph. 3. Use the slope to find another point. 4. Draw a straight line through the points.

Front

What is the standard form of a linear equation?

Back

Ax + By = C, where A, B, and C are integers.

Front

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

Back

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

Front

What does it mean if two lines are parallel?

Back

They have the same slope but different y-intercepts, meaning they will never intersect.