Slope and Writing Linear Equations

Front

What is the slope of a line?

Back

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

What is the slope of parallel lines?

Back

The slopes of parallel lines are the same.

Front

What is the slope of perpendicular lines?

Back

The slopes of perpendicular lines are negative reciprocals of each other (m1 * m2 = -1).

Front

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

Back

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

Front

How do you write the equation of a line given the slope and y-intercept?

Back

Use the slope-intercept form: y = mx + b, substituting the given slope (m) and y-intercept (b).

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

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

Back

Start with point-slope form: y - y1 = m(x - x1) and rearrange to solve for y.