Graphing and Solving Linear Equations

The video tutorial covers solving systems of equations by graphing. It begins with an introduction to systems of equations and demonstrates how to graph them to find intersection points. The tutorial includes examples of graphing equations in slope-intercept form and handling vertical lines. It also shows how to convert equations not in slope-intercept form for graphing. The use of Desmos as a tool for graphing is highlighted, making the process easier. Special cases such as parallel and identical lines are discussed, explaining scenarios with no solution or infinite solutions.

What is the solution to the system of equations where the lines intersect at the point (3, 5)?

• (3, 5)

• (-3, 5)

• (3, -5)

• (5, 3)

In the equation y = mx + b, what does 'm' represent?

• Slope

• Constant

• X-intercept

• Y-intercept

When graphing the equation x = 5, what type of line is drawn?

• No line

• Diagonal line

• Vertical line

• Horizontal line

What is the y-intercept of the equation y = 3x - 7?

• 7

• 3

• -7

• 0

How do you convert the equation 2x - y = 10 to slope-intercept form?

• y = 2x + 10

• y = 2x - 10

• y = -2x + 10

• y = -2x - 10

What is the advantage of using Desmos for graphing systems of equations?

• It does not show the graph

• It automatically highlights intersection points

• It requires solving equations first

• It only graphs one line at a time

What is the solution to the system of equations if the lines intersect at (2, 1)?

• (1, 2)

• (2, 1)

• (2, -1)

• (-2, 1)

What is the solution to a system of equations where the lines are parallel?

• One solution

• No solution

• Two solutions

• Infinite solutions

What happens when two lines in a system of equations are identical?

• They intersect at two points

• They intersect at all points

• They never intersect

• They intersect at one point

Which of the following is a characteristic of parallel lines?

• They have the same slope

• They intersect at one point

• They have different slopes

• They form a right angle