O3C4 Tables, Equations, and Graphs

Front

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

Back

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

Front

How do you find the slope of a line given two points (x1, y1) and (x2, y2)?

Back

The slope (m) is calculated as m = (y2 - y1) / (x2 - x1).

Front

What does the y-intercept represent in a linear equation?

Back

The y-intercept is the point where the line crosses the y-axis, represented by the value of b in the equation y = mx + b.

Front

What is a table of values in relation to a linear equation?

Back

A table of values lists pairs of x and y coordinates that satisfy the linear equation.

Front

How can you determine if a table of values represents a linear function?

Back

If the differences between the y-values are constant for equal intervals of x, the table represents a linear function.

Front

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

Back

The slope indicates the rate of change of y with respect to x; a positive slope means y increases as x increases, while a negative slope means y decreases.

Front

How do you graph a linear equation using its slope and y-intercept?

Back

Start at the y-intercept on the y-axis, then use the slope to determine the rise over run to plot additional points.

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 do you convert a linear equation from standard form to slope-intercept form?

Back

To convert, solve for y to isolate it on one side: y = mx + b.

Front

What is the relationship between the coefficients in the equation y = mx + b and the graph of the line?

Back

The coefficient m represents the slope, and b represents the y-intercept, determining the line's steepness and where it crosses the y-axis.