Slope and y-Intercept

Front

What is the slope in the equation of a line?

Back

The slope is the ratio of the change in y (vertical change) to the change in x (horizontal change) between two points on the line.

Front

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

Back

The y-intercept is the value of y when x is 0, representing the starting point of the line on the y-axis.

Front

Given the equation y = 2x + 3, what is the slope?

Back

The slope is 2.

Front

Given the equation y = -rac{1}{2}x + 4, what is the y-intercept?

Back

The y-intercept is 4.

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

If a line has a slope of 0, what does this mean?

Back

A slope of 0 means the line is horizontal and does not rise or fall.

Front

If a line has an undefined slope, what does this mean?

Back

An undefined slope means the line is vertical, and it does not have a defined rise over run.

Front

What is the slope of the line that passes through the points (1, 2) and (3, 6)?

Back

The slope is 2.