Solving Systems by Graphing in Algebra 2

The video tutorial covers interpreting graph points, graphing linear equations, and solving systems of equations by finding intersection points. It explains common mistakes in graphing, such as incorrect slope usage, and emphasizes the importance of precision. The tutorial also discusses graphing equations in y-intercept form and provides practice problems to reinforce learning. Key concepts include understanding graph coordinates, slope, y-intercept, and identifying solutions in systems of equations.

What does the point (0, 25) represent on the graph?

• The sloth is on the ground at time zero.

• The sloth is 25 feet above the ground at time zero.

• The sloth is 25 feet above the ground after 25 hours.

• The sloth is 25 feet below the ground at time zero.

What does the point (4, 0) indicate about the sloth's position?

• The sloth is 4 feet below the ground after 4 hours.

• The sloth is on the ground after 4 hours.

• The sloth is 4 feet above the ground at time zero.

• The sloth is 4 feet above the ground after 4 hours.

What is the common mistake made when graphing the slope?

• Mixing up the rise and run values.

• Using negative values for both rise and run.

• Using the y-intercept as the slope.

• Starting the graph at the wrong point.

How do you find the solution to a system of linear equations on a graph?

• By finding the y-intercept of each line.

• By finding the x-intercept of each line.

• By finding the slope of each line.

• By finding the intersection point of the lines.

What is the intersection point of the lines y = -4x + 5 and y = 3x - 9?

• (-3, 2)

• (2, 3)

• (3, -2)

• (2, -3)

What should you do first when the equation is not in the form y = mx + b?

• Graph the equation as it is.

• Find the slope and y-intercept directly.

• Solve for x first.

• Solve for y to get it by itself.

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

• (1, 3)

• (3, 1)

• (2, 1)

• (1, 2)

What does it mean if two lines on a graph are parallel?

• They intersect at one point.

• They have the same slope but different y-intercepts.

• They have the same y-intercept.

• They have different slopes but the same y-intercept.

How can you tell if a system of equations has infinitely many solutions?

• The lines have different slopes.

• The lines are the same, meaning they overlap completely.

• The lines intersect at exactly one point.

• The lines are parallel.

What is the solution to the system of equations if the lines intersect at (2, 2)?

• Infinitely many solutions

• No solution

• Two solutions

• One solution