Slope and Y-Intercept

Front

What is the slope of a line?

Back

The slope of a line is a measure of its steepness, typically represented as 'm' in the equation of a line (y = mx + b). It is calculated as the rise over run, or the change in y divided by the change in x.

Front

What does the y-intercept represent in a linear equation?

Back

The y-intercept is the point where the line crosses the y-axis. It is represented as 'b' in the equation of a line (y = mx + b) and indicates the value of y when x is 0.

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 y-intercept of the line represented by the equation y = 2x + 1?

Back

The y-intercept is 1, which is the value of y when x = 0.

Front

If a line has a slope of 0, what does that indicate about the line?

Back

A slope of 0 indicates that the line is horizontal, meaning there is no change in y as x changes.

Front

What does a negative slope indicate about a line?

Back

A negative slope indicates that the line is decreasing, meaning as x increases, y decreases.

Front

What is the slope of a vertical line?

Back

The slope of a vertical line is undefined because the change in x is 0, leading to division by zero.

Front

How can you identify the slope from a graph?

Back

The slope can be identified by selecting two points on the line and calculating the rise (vertical change) over the run (horizontal change).

Front

What is the formula for the slope-intercept form of a linear equation?

Back

The slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept.

Front

If the equation of a line is y = -3x + 4, what is the slope?

Back

The slope is -3.