Modified Point-Slope Form + Inverse Practice

Front

What is the modified point-slope form of a linear equation?

Back

The modified point-slope form is given by the equation: y = m(x - x_0) + y_0, where m is the slope and (x_0, y_0) is a point on the line.

Front

How do you find the equation of a line given a slope and a point?

Back

Use the modified point-slope form: y = m(x - x_0) + y_0, substituting the slope (m) and the coordinates of the point (x_0, y_0).

Front

What is the slope of a line?

Back

The slope of a line is a measure of its steepness, calculated as the ratio of the vertical change to the horizontal change between two points on the line.

Front

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

Back

To convert, expand the point-slope form equation y = m(x - x_0) + y_0 to the form y = mx + b, where b is the y-intercept.

Front

What is the inverse of a function?

Back

The inverse of a function f(x) is a function f^{-1}(x) that reverses the effect of f, such that f(f^{-1}(x)) = x for all x in the domain.

Front

How do you find the inverse of a linear function?

Back

To find the inverse of a linear function f(x) = mx + b, swap x and y, then solve for y: y = (x - b)/m.

Front

What is the significance of the slope in a linear equation?

Back

The slope indicates the direction and steepness of the line; a positive slope means the line rises, while a negative slope means it falls.

Front

What does it mean for two lines to be parallel?

Back

Two lines are parallel if they have the same slope and will never intersect.

Front

What does it mean for two lines to be perpendicular?

Back

Two lines are perpendicular if the product of their slopes is -1, indicating they intersect at a right angle.

Front

How do you determine the slope from two points?

Back

The slope (m) can be calculated using the formula m = (y_2 - y_1) / (x_2 - x_1), where (x_1, y_1) and (x_2, y_2) are the coordinates of the two points.