8.3.b: Slope Intercept Form

Front

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

Back

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

Front

What does the slope (m) represent in the slope-intercept form?

Back

The slope (m) represents the rate of change of y with respect to x, indicating how steep the line is.

Front

What does the y-intercept (b) represent in the slope-intercept form?

Back

The y-intercept (b) represents the point where the line crosses the y-axis.

Front

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

Back

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

Front

If a line has a positive slope, what does that indicate about the relationship between x and y?

Back

A positive slope indicates that as x increases, y also increases.

Front

If a line has a negative slope, what does that indicate about the relationship between x and y?

Back

A negative slope indicates that as x increases, y decreases.

Front

What is the significance of a slope of zero?

Back

A slope of zero indicates a horizontal line, meaning there is no change in y as x changes.

Front

What is the significance of an undefined slope?

Back

An undefined slope indicates a vertical line, meaning x remains constant while y changes.

Front

How can you write the equation of a line given a slope and a point on the line?

Back

You can use the point-slope form: y - y1 = m(x - x1), where (x1, y1) is the point and m is the slope.

Front

What is the relationship between parallel lines in terms of slope?

Back

Parallel lines have the same slope but different y-intercepts.