CI: Linear Functions Review

Front

What is the equation of a line in point-slope form?

Back

The point-slope form of a line is given by the equation: y - y_1 = m(x - x_1), where m is the slope and (x_1, y_1) is a point on the line.

Front

Given a slope of ⅔ and a point (-4, 7), what is the point-slope form of the line?

Back

The equation is: y - 7 = \frac{2}{3}(x + 4).

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) where b is the y-coordinate.

Front

How do you find the y-intercept from the equation of a line?

Back

To find the y-intercept, set x = 0 in the equation of the line and solve for y.

Front

What is the slope of a line?

Back

The slope of a line measures its steepness and is calculated as the change in y divided by the change in x (rise/run).

Front

What does a positive slope indicate about a line?

Back

A positive slope indicates that as x increases, y also increases, resulting in an upward slant 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, resulting in a downward slant from left to right.

Front

What is the formula to calculate the slope between two points (x1, y1) and (x2, y2)?

Back

The slope m is calculated as m = \frac{y_2 - y_1}{x_2 - x_1}.

Front

What is the standard form of a linear equation?

Back

The standard form of a linear equation is Ax + By = C, where A, B, and C are integers.

Front

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

Back

To convert, solve for y in the point-slope equation: y - y_1 = m(x - x_1) to get y = mx + b.