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 represents 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 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 does it mean if the slope of a line is positive?

Back

If the slope of a line is positive, it means that as x increases, y also increases, indicating an upward trend.

Front

What does it mean if the slope of a line is negative?

Back

If the slope of a line is negative, it means that as x increases, y decreases, indicating a downward trend.

Front

What is the relationship between parallel lines and their slopes?

Back

Parallel lines have the same slope but different y-intercepts. They never intersect.

Front

What is the relationship between perpendicular lines and their slopes?

Back

Perpendicular lines have slopes that are negative reciprocals of each other. If one slope is m, the other is -1/m.

Front

How can you determine the y-intercept from a linear equation in slope-intercept form?

Back

In the slope-intercept form y = mx + b, the y-intercept is the value of b.