Foundations Final: Calculator Active

Front

What is the formula to find the midpoint of a line segment with endpoints (x1, y1) and (x2, y2)?

Back

The midpoint M is given by M = \left(\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2}\right).

Front

What does it mean for two lines to be perpendicular in a coordinate plane?

Back

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

Front

How do you find the slope of a line given its equation in the form Ax + By = C?

Back

Rearrange the equation to slope-intercept form (y = mx + b) to find the slope m = -\frac{A}{B}.

Front

What is the y-intercept of a linear function?

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 determine if one function has a larger y-intercept than another?

Back

Compare the b-values in the slope-intercept form of both functions.

Front

What is the equation of a line that is perpendicular to the line y = mx + b and passes through a point (x1, y1)?

Back

The equation is y - y_1 = -\frac{1}{m}(x - x_1).

Front

What is the general form of a linear function?

Back

A linear function can be expressed as f(x) = mx + b, where m is the slope and b is the y-intercept.

Front

How do you combine two linear functions to find a total function?

Back

Add the corresponding outputs of the functions: h(x) = f(x) + g(x).

Front

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

Back

The slope indicates the rate of change of the function; a positive slope means the function is increasing, while a negative slope means it is decreasing.

Front

How do you find the value of k for a line that is perpendicular to another line?

Back

Use the negative reciprocal of the slope of the given line to find the slope of the perpendicular line, then use a point on the line to solve for k.