Slope & Linear Functions

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). 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

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

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 slope of the line that passes through the points (2, 3) and (4, 7)?

Back

The slope is 2, calculated as (7 - 3) / (4 - 2).

Front

What is the slope of the line that passes through the points (1, 2) and (1, 5)?

Back

The slope is undefined because the x-coordinates are the same, indicating a vertical line.

Front

What is the y-intercept in the equation y = mx + b?

Back

The y-intercept (b) is the point where the line crosses the y-axis, represented by the value of y when x = 0.

Front

What type of slope does a horizontal line have?

Back

A horizontal line has a slope of 0, indicating that y remains constant as x changes.

Front

What type of slope does a vertical line have?

Back

A vertical line has an undefined slope because the change in x is zero.

Front

Is the equation y = 3x + 2 a linear relationship?

Back

Yes, it is a linear relationship because it can be expressed in the form y = mx + b.