Solving Proportional Relationships and Equations

This video tutorial covers Math 8 Unit 4 Lesson 6, focusing on strategic solving of linear equations. It begins with an activity on equal perimeters, where students solve for x and find perimeters of shapes. The lesson progresses to predicting solutions without solving, determining if they are positive, negative, or zero. Students then choose equations based on difficulty and solve them, followed by homework problems with detailed solutions. The lesson concludes with exploring proportional relationships, completing tables, and graphing equations.

What is the value of x if the perimeters of a triangle and a square are equal, given the triangle's sides are 2x, 2x, and x-8, and the square's side is x+2?

• x = 8

• x = 24

• x = 32

• x = 16

In the context of predicting solutions, what is the value of x when both sides of an equation have the same x coefficient?

• Negative

• Zero

• Positive

• Undefined

Which of the following equations is considered least difficult to solve due to the absence of fractions and decimals?

• Equation C

• Equation A

• Equation B

• Equation D

What is the solution for the equation 2 * (4k + 3) - 3 = 2 * (18 - k) - 3?

• k = 2

• k = 4

• k = 3

• k = 1

When solving the equation 10 - v/4 = 2 * v + 17, what is the value of v?

• v = -7

• v = 14

• v = -14

• v = 7

What is the solution for the equation -3b + 11 = 8b - 18?

• b = 29/11

• b = 18/8

• b = 8/18

• b = 11/29

In the equation 9x + 15 = 3x + 15, what is the solution for x?

• x = 0

• x = 1

• x = 2

• No solution

What is the constant of proportionality (k) if y = 3/2x in a proportional relationship?

• k = 1

• k = 2

• k = 3/2

• k = 3

If a table of values shows a proportional relationship, what should the graph of this relationship look like?

• A horizontal line

• A curve

• A straight line through the origin

• A vertical line

What is the y-value when x = 64 in a proportional relationship with k = 3/2?

• y = 48

• y = 32

• y = 96

• y = 64