Equations of a line

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 write the equation of a line in slope-intercept form?

Back

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

Front

What is the y-intercept in the equation y = -4x - 5?

Back

The y-intercept is -5, which is the value of y when x = 0.

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 point-slope form of a line?

Back

Point-slope form is written as y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope.

Front

Convert the point-slope form y + 7 = -1/4(x - 4) to slope-intercept form.

Back

To convert, distribute and simplify: y = -1/4x + 1 - 7, which simplifies to y = -1/4x - 6.

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

How do you determine if two lines are parallel?

Back

Two lines are parallel if they have the same slope but different y-intercepts.

Front

How do you determine if two lines are perpendicular?

Back

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