Graphing Equations

Front

What is the slope of a line?

Back

The slope of a line is a measure of its steepness, typically represented as 'm' in the equation of a line (y = mx + b). It is calculated as the change in y divided by the change in x (rise/run).

Front

How do you find the slope using counting?

Back

To find the slope using counting, select two points on the line, count the vertical change (rise) and the horizontal change (run) between them, and then divide the rise by the run.

Front

What does the equation y = -x + 2 represent?

Back

This equation represents a straight line with a slope of -1 and a y-intercept of 2. It decreases as x increases.

Front

What is the solution to a system of equations?

Back

The solution to a system of equations is the point where the graphs of the equations intersect, representing the values of the variables that satisfy all equations in the system.

Front

What does it mean if a system of equations has no solution?

Back

If a system of equations has no solution, it means that the lines represented by the equations are parallel and will never intersect.

Front

What is the y-intercept in the equation of a line?

Back

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

Front

How do you graph the equation y = mx + b?

Back

To graph y = mx + b, start at the y-intercept (0, b) on the y-axis, then use the slope (m) to find another point by moving up/down and left/right.

Front

What is the difference between intersecting lines and parallel lines?

Back

Intersecting lines cross each other at one point, while parallel lines never meet and have the same slope.

Front

How can you determine if two lines are parallel from their equations?

Back

Two lines are parallel if they have the same slope (m) in their equations, even if their y-intercepts (b) are different.

Front

What is the graphical representation of the equation y = 2?

Back

The equation y = 2 represents a horizontal line that crosses the y-axis at 2.