Solving Linear Equations and Relationships

This video tutorial covers Math 8 Unit 4 Lesson 6 on strategic solving of linear equations. It begins with an introduction to solving linear equations and an activity on equal perimeters. The lesson progresses to predicting solutions without solving, determining if they are positive, negative, or zero. Students are then guided to choose equations based on difficulty and solve them. The video also includes solutions to homework problems and explores proportional relationships, including graphing them.

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

• x = 32

• x = 24

• x = 16

• x = 8

If an equation has the same x value on both sides, what is the solution likely to be?

• Negative

• Undefined

• Positive

• Zero

Which of the following equations is likely to be the easiest to solve?

• Equation with fractions

• Equation with complex variables

• Equation with decimals

• Equation with simple distribution

In solving the equation 2(4k + 3) - 3 = 2(18 - k) - 3, what is the value of k?

• k = 1

• k = 2

• k = 4

• k = 3

What is the solution for the equation 10 - v/4 = 2v + 17?

• v = 14

• v = -14

• v = 7

• v = 0

What is the value of b in the equation -3b + 11 = 8b - 18?

• b = 8/18

• b = 29/11

• b = 11/29

• b = 18/8

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

• No solution

• x = 2

• x = 1

• x = 0

What is the constant of proportionality (k) if y = 3/2x and y = 21 when x = 14?

• k = 2

• k = 2/3

• k = 3/2

• k = 1

How do you graph a proportional relationship given the equation y = 3/2x?

• Use a calculator

• Plot random points

• Start at y-intercept and use the slope

• Start at the origin and use the slope

If you have a table of values for x and y in a proportional relationship, how do you find the missing y value for a given x?

• Divide x by the constant of proportionality

• Subtract x from the constant of proportionality

• Add x to the constant of proportionality

• Multiply x by the constant of proportionality