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Chapter 3: Problem 24

Complete each ordered pair for the equation \(y=2 x+7\) $$ (2,___) $$

Short Answer

Expert verified
(2, 11)

Step by step solution

01

Understand the given equation

The given equation is a linear equation in the form of y = 2x + 7. In this exercise, substitute the value of x from the ordered pair (2, ___) into the equation to find y.
02

Substitute x into the equation

Substitute x = 2 into the equation y = 2x + 7. This yields: y = 2(2) + 7.
03

Simplify the expression

Calculate the value obtained in the previous step: y = 2(2) + 7 = 4 + 7 = 11.
04

Complete the ordered pair

Now that we have the value of y, the complete ordered pair is (2, 11).

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

ordered pairs
An ordered pair is a set of two numbers in a specific order. Usually, this is written as (x, y).
The first number (x) is the 'x-coordinate,' and the second number (y) is the 'y-coordinate.'
Ordered pairs are used to represent points on a graph. For instance, in this exercise, (2, ___) means that the x-coordinate is 2, and we need to find the y-coordinate.
substitution method
The substitution method involves replacing a variable (like x) with a specific number to solve an equation.
For example, in our exercise, we have the equation: y = 2x + 7.
Here, we substitute x = 2 to find the value of y.
So, our equation becomes y = 2(2) + 7.
Calculate: y = 4 + 7 = 11. Therefore, when x is 2, y is 11, giving us the ordered pair (2, 11).
Substitution helps in pinpointing exact values in equations.
linear equations
A linear equation is an equation that makes a straight line when it is graphed.
It usually looks like y = mx + b, where:
  • 'm' is the slope of the line.
  • 'b' is the y-intercept.
  • x and y are variables.
In our exercise, y = 2x + 7 is a linear equation.

This means:
  • For every 1 unit increase in x, y increases by 2 units (the slope, m, is 2).
  • The line crosses the y-axis at 7 (the y-intercept, b, is 7).
Linear equations are fundamental in algebra and help in understanding more complex mathematical concepts.

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