Solving Systems of Equations by Graphing

Front

What are parallel lines?

Back

Parallel lines are lines in a plane that never intersect. They have the same slope.

Front

What does it mean for two lines to intersect?

Back

Two lines intersect if they cross each other at a point, meaning they have different slopes.

Front

How do you find the y-intercept of a line?

Back

The y-intercept is the point where the line crosses the y-axis, found by setting x=0 in the equation of the line.

Front

What is the solution to a system of equations?

Back

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

Front

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

Back

A system has no solution if the lines are parallel and never intersect.

Front

What does it mean if a system of equations has infinitely many solutions?

Back

A system has infinitely many solutions if the lines are coincident, meaning they lie on top of each other.

Front

How do you graph a linear equation?

Back

To graph a linear equation, find two or more points that satisfy the equation and connect them with a straight line.

Front

What is the slope of a line?

Back

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

Front

What is the formula for slope?

Back

The formula for slope (m) is m = (y2 - y1) / (x2 - x1) for two points (x1, y1) and (x2, y2).

Front

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

Back

Two lines are parallel if they have the same slope in their slope-intercept form (y = mx + b).