Parallel - Linear Equations

Front

What are parallel lines?

Back

Parallel lines are lines in a plane that never meet or intersect, no matter how far they are extended.

Front

What is the slope of a line?

Back

The slope of a line is a measure of its steepness, usually represented as 'm' in the equation of a line (y = mx + b).

Front

What does it mean for two lines to be parallel in terms of their slopes?

Back

Two lines are parallel if they have the same slope (m) but different y-intercepts (b).

Front

If two lines have different slopes, what can be said about their relationship?

Back

If two lines have different slopes, they are not parallel and will eventually intersect.

Front

What is the general form of a linear equation?

Back

The general form of a linear equation is y = mx + b, where m is the slope and b is the y-intercept.

Front

How can you determine if two lines are parallel from their equations?

Back

To determine if two lines are parallel, compare their slopes. If the slopes are equal, the lines are parallel.

Front

What is the y-intercept of a line?

Back

The y-intercept of a line is the point where the line crosses the y-axis, represented as 'b' in the equation y = mx + b.

Front

Given the equations y = 3x + 2 and y = 3x - 4, are they parallel?

Back

Yes, they are parallel because they have the same slope (3) and different y-intercepts.

Front

What happens to the graph of a line if the slope is zero?

Back

If the slope is zero, the graph of the line is horizontal.

Front

What is the significance of the slope in real-world applications?

Back

The slope represents the rate of change, such as speed in a distance-time graph or cost per item in a pricing model.