Slope and Point-Slope Review

Front

What is the slope of a line?

Back

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

Front

How do you find 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 linear equation?

Back

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

Front

Convert the slope-intercept form to point-slope form: y = 2x + 3.

Back

Point-slope form can be derived from a point on the line, e.g., using the point (0, 3): y - 3 = 2(x - 0).

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 that mean?

Back

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

Front

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

Back

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

Front

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

Back

The slope is m = (7 - 3) / (4 - 2) = 4 / 2 = 2.

Front

Write the equation in point-slope form for a line with slope 3 passing through the point (1, 2).

Back

The equation is y - 2 = 3(x - 1).