Slope & y=mx+b & Proportional Relationships

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 y=mx+b. It is calculated as the change in y divided by the change in x (rise/run).

Front

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

Back

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

Front

What does the equation y=mx+b represent?

Back

This is the slope-intercept form of a linear equation, where 'm' is the slope and 'b' is the y-intercept.

Front

What is a proportional relationship?

Back

A proportional relationship is one where two quantities maintain a constant ratio, meaning as one quantity changes, the other changes at a consistent rate.

Front

What is a non-proportional relationship?

Back

A non-proportional relationship does not maintain a constant ratio between two quantities; the rate of change varies.

Front

If a line passes through (1, 2) and (3, 6), what is the slope?

Back

Slope = (6 - 2) / (3 - 1) = 4 / 2 = 2.

Front

What does a positive slope indicate about a line?

Back

A positive slope indicates that as x increases, y also increases, meaning the line rises from left to right.

Front

What does a negative slope indicate about a line?

Back

A negative slope indicates that as x increases, y decreases, meaning the line falls from left to right.

Front

What is the y-intercept in the equation y=3x+4?

Back

The y-intercept is 4, which is the value of y when x=0.

Front

How can you tell if a relationship is linear?

Back

A relationship is linear if it can be represented by a straight line on a graph.