Linear Equations and Their Properties

The video tutorial covers a practice problem from lesson 14 on solving systems of linear equations. It explains how different slopes affect the number of solutions in a system, using both algebraic and graphical methods. A contextual story problem involving two siblings walking to a park is used to illustrate these concepts. The video also reviews how to determine solutions using standard form equations.

What happens when two linear equations have different slopes?

• They have no solutions.

• They have exactly one solution.

• They have infinite solutions.

• They are identical.

If two equations have the same slope but different y-intercepts, what is true about their graphs?

• They are parallel.

• They intersect at one point.

• They form a circle.

• They are identical.

In the context of Juan and Annie, what does the y-intercept represent?

• Their walking speed.

• The distance from the park.

• The time taken to reach the park.

• The slope of the line.

How long does it take Annie to reach the park?

• 1 hour

• 1.5 hours

• 2 hours

• 2.5 hours

What is the slope of Juan's walking equation?

• -1.5

• 2

• -2

• 1.5

How do you calculate the slope from the standard form of an equation?

• Divide the y-intercept by the x-coefficient.

• Take the opposite of the x-coefficient divided by the y-coefficient.

• Add the x and y coefficients.

• Multiply the x and y coefficients.

What is the y-intercept of the equation 3x + 2y = 6?

• 2

• 6

• 0

• 3

Which equation forms a system with a single solution with y = -1.5x + 3?

• y = -1.5x + 6

• y = -1.5x

• y = -1.5x + 0

• y = -2x + 3

What is the significance of the point where two graphs intersect?

• It represents the y-intercept.

• It is the solution to the system of equations.

• It is the midpoint of the lines.

• It is the x-intercept.

What does a negative slope indicate in the context of Juan and Annie's walk?

• They are stationary.

• They are walking in a circle.

• They are walking towards the park.

• They are walking away from the park.