ch 3 big ideas

Front

What is the formula for calculating the slope of a line?

Back

The slope (m) of a line is calculated using the formula m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are two points on the line.

Front

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

Back

To find the y-intercept of a linear equation in the form y = mx + b, set x = 0 and solve for y. The y-intercept is the value of y when x is 0.

Front

What are x- and y-intercepts?

Back

The x-intercept is the point where the graph crosses the x-axis (y=0), and the y-intercept is where the graph crosses the y-axis (x=0).

Front

What is the vertical line test?

Back

The vertical line test is a method to determine if a graph represents a function. If any vertical line intersects the graph at more than one point, it is not a function.

Front

What is a function?

Back

A function is a relation that assigns exactly one output (y) for each input (x).

Front

What is the slope of a line that rises 3 units for every 4 units it runs?

Back

The slope of the line is 3/4.

Front

How can you determine if a mapping is a function?

Back

A mapping is a function if each input is associated with exactly one output. If any input corresponds to multiple outputs, it is not a function.

Front

What does it mean for a function to be linear?

Back

A linear function is a function that can be graphically represented as a straight line, typically in the form y = mx + b.

Front

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

Back

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

Front

How do you convert the standard form of a linear equation to slope-intercept form?

Back

To convert from standard form (Ax + By = C) to slope-intercept form (y = mx + b), solve for y.