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Big Ideas Math: Modeling Real Life, Grade 8

BI

Big Ideas Math: Modeling Real Life, Grade 8 View details

Cumulative Practice

Exercise 2 Page 193

What is the meaning of the ordered pair?

H

Consider the given equation. 6x-5y=14 We want to find which of the given points lie on the graph of the equation. To do so, let's substitute each point into the given equation to see if it satisfies the equality. We will start with (- 4,- 1).

6x-5y=14

x= - 4, y= - 1

6( - 4)-5( - 1)? =14

a(- b)=- a * b

- 6 * 4 - (- 5 * 1)? =14

Multiply

- 24 - (- 5)? =14

a-(- b)=a+b

- 24 +5 ? =14

Add terms

- 19≠ 14

This means that the point (- 4,- 1) does not lie on the graph. The next point is (- 2,4).

6x-5y=14

x= - 2, y= 4

6( - 2)-5( 4)? =14

a(- b)=- a * b

- 6 * 2 - 5(4)? =14

Multiply

- 12- 20 ? =14

Subtract term

- 32 ≠ 14

As we can see, the equality is not true. This point does not lie on the graph of the given equation. Now, we will substitute (- 1,- 4) into the equation.

6x-5y=14

x= - 1, y= - 4

6( - 1)-5( - 4)? =14

a(- b)=- a * b

- 6 * 1 - (- 5 * 4)? =14

Multiply

- 6 - (- 20)? =14

a-(- b)=a+b

- 6+20 ? =14

Add terms

14= 14

Since the equality is true, the point (- 1, - 4) lies on the graph. Finally, let's check the last point, (4,- 2).

6x-5y=14

x= 4, y= - 2

6( 4)-5( - 2)? =14

a(- b)=- a * b

6(4) - (- 5 * 2)? =14

Multiply

24 - (- 10)? =14

a-(- b)=a+b

24 +10 ? =14

Add terms

34≠ 14

Therefore, the correct option is H.

Extra

Linear Equations

A linear equation is an equation whose graph is a line.

This type of equation contains at least one linear term and any number of constants. Let's see a few examples! & y=2x+1, & 3x=6 +3, & 2y+x=4 For those of you who are interested in learning more about the different types of linear equations and their graphs, you can read more about them on the following pages.

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Exercises