Systems: Graphing

Front

What is the slope of a line?

Back

The slope of a line is a measure of its steepness, calculated as the change in y divided by the change in x (rise over run).

Front

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

Back

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

Front

What does the y-intercept represent in the equation of a line?

Back

The y-intercept is the point where the line crosses the y-axis, represented by the value of y when x = 0.

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

What is the difference between a solution to a system of equations and a solution to a single equation?

Back

A solution to a system of equations satisfies all equations in the system, while a solution to a single equation satisfies only that equation.

Front

How can you determine if a point is a solution to a system of equations?

Back

Substitute the point's coordinates into each equation; if it satisfies all equations, it is a solution.

Front

What does it mean for two lines to be parallel?

Back

Two lines are parallel if they have the same slope and 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.

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 (b) and use the slope (m) to find another point.

Front

What is the significance of the coordinates (x, y) in a graph?

Back

The coordinates (x, y) represent a specific point on the graph, where x is the horizontal position and y is the vertical position.