Finding Slope and Writing Linear Equations

Front

What is the definition of slope?

Back

Slope is a measure of the steepness of a line, calculated as the change in y divided by the change in x (rise/run).

Front

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

Back

Slope (m) = (y2 - y1) / (x2 - x1).

Front

What is the y-intercept of a line?

Back

The y-intercept is the point where the line crosses the y-axis, represented as (0, b) in the equation y = mx + b.

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 m is the slope and (x1, y1) is a point on the line.

Front

Convert the point-slope form to slope-intercept form: y - 2 = 3(x + 1).

Back

y = 3x + 5.

Front

What does the slope of a line indicate about its direction?

Back

A positive slope indicates the line rises from left to right, while a negative slope indicates it 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.

Front

What is the formula for writing the equation of a line given a slope and a point?

Back

Use the point-slope form: y - y1 = m(x - x1).

Front

How do you determine if two lines are parallel?

Back

Two lines are parallel if they have the same slope.

Front

How do you determine if two lines are perpendicular?

Back

Two lines are perpendicular if the product of their slopes is -1.