Graphing Systems of Equations

Front

What is a system of equations?

Back

A set of two or more equations with the same variables.

Front

What does it mean for two lines to intersect?

Back

It means they have one solution, which is the point where they cross.

Front

What is the graphical representation of a linear equation?

Back

A straight line on a coordinate plane.

Front

What does it mean if two lines are parallel?

Back

They have no solutions because they never intersect.

Front

How can you determine the solution of a system of equations by graphing?

Back

By finding the point where the two lines intersect.

Front

What is the solution to the system of equations y = 2x + 1 and y = -x + 4?

Back

(1, 3) - The lines intersect at this point.

Front

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

Back

The lines are parallel and do not intersect.

Front

What is the slope of a line?

Back

The rate at which y changes for a change in x, often represented as 'm' in the equation y = mx + b.

Front

What is the y-intercept of a line?

Back

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

Front

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

Back

Start at the y-intercept (b) and use the slope (m) to find another point.