Writing Equations from Graphs & Tables

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 (positive slope goes up, negative slope goes down).

Front

What does the y-intercept (b) represent 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 determine the slope from a graph?

Back

To determine the slope from a graph, pick two points on the line, calculate the rise (change in y) and run (change in x), and use the formula slope = rise/run.

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, and A should be non-negative.

Front

How can you write an equation from a table of values?

Back

To write an equation from a table of values, identify the slope by calculating the change in y over the change in x, then use one of the points to find the y-intercept.

Front

What is the difference between positive and negative slopes?

Back

A positive slope means that as x increases, y also increases, resulting in an upward line. A negative slope means that as x increases, y decreases, resulting in a downward line.

Front

What does it mean for two lines to be parallel?

Back

Two lines are parallel if they have the same slope but different y-intercepts, meaning they will never intersect.

Front

What does it mean for two lines to be perpendicular?

Back

Two lines are perpendicular if the product of their slopes is -1, meaning one line has a positive slope and the other has a negative slope.

Front

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

Back

To convert from slope-intercept form (y = mx + b) to standard form (Ax + By = C), rearrange the equation to get all terms on one side.