Sisters' Distance and Graph Intersections

The video tutorial covers solving a practice problem from lesson 13 on systems of equations. It involves two sisters riding towards each other on bicycles, starting 21 miles apart. The video explains how to calculate the time and point where they meet using both graphical and algebraic methods. The key concepts include understanding rates, y-intercepts, and slopes, and applying these to find the solution. The tutorial also demonstrates the use of division and multiplication to solve the problem, providing a comprehensive understanding of the mathematical principles involved.

What is the combined rate at which the two sisters are riding towards each other?

• 3/2 miles per hour

• 2 miles per hour

• 1 mile per hour

• 5/4 miles per hour

How far apart are the two sisters initially?

• 6 miles

• 14 miles

• 21 miles

• 19 miles

What is the difference in the y-intercepts of the two graphs?

• 19 units

• 21 units

• 14 units

• 6 units

How is the difference in slopes calculated?

• 5/4 minus 1/4

• 5/4 plus 1/4

• 5/4 minus (-1/4)

• 5/4 plus (-1/4)

What is the simplified form of six-fourths?

• 3/2

• 2

• 5/4

• 1

How many units along the x-axis do the graphs need to move to intersect?

• 7 units

• 14 units

• 21 units

• 3 units

What is the x-coordinate of the intersection point?

• 3

• 14

• 21

• 7

What is the y-coordinate of the intersection point?

• 14

• 15.5

• 17.5

• 16

Which equation is used to find the y-coordinate after finding x?

• y = 5/4x - 2

• y = -1/4x + 19

• y = 5/4x + 19

• y = -1/4x - 2

What is the final solution for the coordinate pair where the graphs intersect?

• (14, 17.5)

• (7, 3)

• (21, 14)

• (14, 15.5)