Warm Up: Graphing Systems of Equations

Front

What happens when you graph the same linear equation twice?

Back

You will have infinite solutions.

Front

What is the first step in solving a system of equations by graphing?

Back

Write both linear equations in slope-intercept form.

Front

What is the solution to the system of equations represented by the point (1, -1)?

Back

The solution is (1, -1).

Front

What is the solution to the system of equations represented by the point (1, 3)?

Back

The solution is (1, 3).

Front

What are the steps for graphing a line given an equation in slope-intercept form?

Back

1. Plot the y-intercept. 2. Count the slope ratio to plot the second point. 3. Draw the line.

Front

What is slope-intercept form of a linear equation?

Back

The slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept.

Front

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

Back

The slope (m) is calculated as m = (y2 - y1) / (x2 - x1).

Front

What does it mean if two lines are parallel when graphing systems of equations?

Back

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

Front

What does it mean if two lines intersect at a single point when graphing systems of equations?

Back

If two lines intersect at a single point, that point is the unique solution to the system.

Front

What is the y-intercept of a line?

Back

The y-intercept is the point where the line crosses the y-axis, represented as (0, b) in slope-intercept form.