13.1 Graphing linear equations

Front

What is a linear equation?

Back

A linear equation is an equation that makes a straight line when graphed. It can be written in the form y = mx + b, where m is the slope and b is the y-intercept.

Front

What does the slope (m) represent in a linear equation?

Back

The slope (m) represents the rate of change of y with respect to x. It indicates how steep the line is and the direction it goes (upward or downward).

Front

What is the y-intercept (b) in a linear equation?

Back

The y-intercept (b) is the point where the line crosses the y-axis. It represents the value of y when x is 0.

Front

How do you find the slope from two points (x1, y1) and (x2, y2)?

Back

The slope (m) can be calculated using the formula m = (y2 - y1) / (x2 - x1).

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 determine if a table of values represents a linear relationship?

Back

A table represents a linear relationship if the differences between consecutive y-values divided by the differences between consecutive x-values are constant.

Front

What does it mean for a graph to be a function?

Back

A graph is a function if every x-value has exactly one corresponding y-value. This means that no vertical line can intersect the graph more than once.

Front

What is the significance of the point (0, b) on a graph of a linear equation?

Back

The point (0, b) is the y-intercept of the graph, indicating where the line crosses the y-axis.

Front

How do you graph a linear equation in slope-intercept form?

Back

To graph a linear equation in slope-intercept form (y = mx + b), start at the y-intercept (0, b) and use the slope (rise/run) to find another point.

Front

What is the relationship between the coefficients of a linear equation and its graph?

Back

The coefficients determine the slope and y-intercept of the line, affecting its steepness and position on the graph.