Proportional Relationships and Slope

Front

What is a proportional relationship?

Back

A proportional relationship is a relationship between two quantities where the ratio of one quantity to the other quantity is constant.

Front

What is the unit rate?

Back

The unit rate is the ratio of two measurements in which the second measurement is 1. For example, if a car travels 60 miles in 1 hour, the unit rate is 60 miles per hour.

Front

What does the slope of a line represent?

Back

The slope of a line represents the rate of change of the y-coordinate with respect to the x-coordinate. It indicates how steep the line is.

Front

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

Back

The slope (m) is calculated using the formula: m = (y2 - y1) / (x2 - x1).

Front

What is the origin in a coordinate plane?

Back

The origin is the point where the x-axis and y-axis intersect, represented by the ordered pair (0,0).

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 is the y-intercept?

Back

The y-intercept is the point where a line crosses the y-axis. It is represented by the value of y when x = 0.

Front

What does it mean for a graph to be proportional?

Back

A graph is proportional if it passes through the origin (0,0) and has a constant slope.

Front

If a line has a slope of 1/2, what does this mean?

Back

A slope of 1/2 means that for every 2 units you move horizontally to the right, you move 1 unit up vertically.

Front

What is the difference between positive and negative slope?

Back

A positive slope means the line rises as it moves from left to right, while a negative slope means the line falls as it moves from left to right.