Solving Linear Systems by Graphing

The video tutorial explains how to graph linear equations and solve systems of equations graphically. It begins with graphing the equation y = x + 3, identifying its slope and y-intercept, and then moves on to graph y = -x + 3. The tutorial demonstrates how to find the intersection of these lines to solve the system of equations. It further explores another set of equations, y = 3x - 6 and y = -x + 6, using similar graphing techniques to find their intersection point. The video emphasizes understanding the graphical nature of solving systems of equations.

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

• (3, 1)

• (1, 3)

• (3, 0)

• (0, 3)

Tags

CCSS.8.EE.B.6

CCSS.8.F.A.3

What does the slope of 1 indicate in the equation y = x + 3?

• For every 1 unit increase in x, y increases by 1 unit.

• For every 1 unit increase in y, x increases by 1 unit.

• For every 1 unit increase in x, y decreases by 1 unit.

• For every 1 unit increase in y, x decreases by 1 unit.

Tags

CCSS.HSF.LE.B.5

What is the slope of the equation y = -x + 3?

• 3

• 1

• -1

• 0

Tags

CCSS.8.EE.B.5

Which point satisfies both equations y = x + 3 and y = -x + 3?

• (0, 3)

• (3, 0)

• (1, 4)

• (-3, 0)

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

What method is used to solve the system of equations graphically?

• Finding the intersection point of the lines

• Calculating the area under the curves

• Determining the slopes of the lines

• Using the Pythagorean theorem

Tags

CCSS.8.EE.C.8B

What is the y-intercept of the equation y = 3x - 6?

• (3, -6)

• (-6, 0)

• (-6, 3)

• (0, -6)

Tags

CCSS.8.EE.B.6

CCSS.8.F.A.3

What is the slope of the equation y = 3x - 6?

• 3

• -3

• 6

• -6

Tags

CCSS.8.EE.B.5

At which point do the lines y = 3x - 6 and y = -x + 6 intersect?

• (-3, -3)

• (3, 3)

• (6, 6)

• (0, 0)

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

What does the intersection point of two lines in a system of equations represent?

• The point where both lines start

• The maximum values of x and y

• The minimum values of x and y

• A solution that satisfies both equations

Tags

CCSS.8.EE.C.8B

How can you verify if a point is a solution to both equations in a system?

• By substituting the point into both equations

• By calculating the area between the lines

• By measuring the distance from the origin

• By drawing a circle through the point