Solving Systems by Graphing

Front

What is the y-intercept of a graph?

Back

The y-intercept is the point where a line crosses the y-axis, represented as (0, y).

Front

How do you find the solution to a system of equations graphically?

Back

The solution is found at the point where the two lines intersect on the graph.

Front

What does it mean if two lines are parallel in a system of equations?

Back

If two lines are parallel, they have no solution because they never intersect.

Front

What is the significance of the point of intersection in a graph of two equations?

Back

The point of intersection represents the solution to the system of equations.

Front

How can you determine the y-intercept from an equation in slope-intercept form (y = mx + b)?

Back

The y-intercept is the value of b in the equation, represented as (0, b).

Front

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

Back

It means that the lines representing the equations are parallel and do not intersect.

Front

What is the solution to the system of equations represented by the lines y = 2x + 1 and y = -x + 3?

Back

The solution is the point where the two lines intersect, which can be found by solving the equations simultaneously.

Front

How do you graph a linear equation?

Back

To graph a linear equation, find the y-intercept, plot it, and use the slope to find another point.

Front

What is the slope of a line?

Back

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

Front

What does it mean if two lines intersect at a single point?

Back

It means that there is exactly one solution to the system of equations represented by those lines.