Slope Intercept and Point Slope Form of a Line

Front

What is the slope-intercept form of a line?

Back

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

Front

What does the slope of a line represent?

Back

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

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 point-slope form of a line?

Back

The point-slope form of a line is given by the equation y - y1 = m(x - x1), where m is the slope and (x1, y1) is a point on the line.

Front

What is the y-intercept of a line?

Back

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

Front

How do you convert from point-slope form to slope-intercept form?

Back

To convert, solve for y in the point-slope equation y - y1 = m(x - x1) to get y = mx + (y1 - mx1).

Front

What is the equation of a line with a slope of 2 that passes through the point (3, 5)?

Back

Using point-slope form: y - 5 = 2(x - 3) simplifies to y = 2x - 1.

Front

If a line has a slope of -1, what does this indicate about its direction?

Back

A slope of -1 indicates that the line descends from left to right at a 45-degree angle.

Front

What is the slope of a horizontal line?

Back

The slope of a horizontal line is 0, indicating no vertical change as x changes.

Front

What is the slope of a vertical line?

Back

The slope of a vertical line is undefined, as it does not have a defined rate of change.