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Chapter 2: Problem 21

Determine the \(y\) -intercept. $$ y=17 x+138 $$

Short Answer

Expert verified
The y-intercept is 138.

Step by step solution

01

- Understand the y-intercept

The y-intercept is the point where the graph of the equation crosses the y-axis. This occurs when the value of x is 0.
02

- Substitute x with 0

To find the y-intercept, substitute 0 for x in the equation y = 17x + 138.
03

- Calculate the y-intercept

Substitute x = 0 in the equation: y = 17(0) + 138 Simplify the equation: y = 138.

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Key Concepts

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

linear equations
A linear equation represents a direct relationship between two variables, typically x and y. In its simplest form, a linear equation looks like this: \( y = mx + b \). Here's what each part means:
  • \( m \) is the slope or the rate of change. It indicates how steep the line is.
  • \( b \) is the y-intercept. It's where the line crosses the y-axis.
Linear equations produce a straight line when graphed. This makes them predictable and easy to work with. They are widely used in various fields like economics, physics, and everyday calculations to represent relationships between quantities.
graphing
Graphing a linear equation involves plotting points on a coordinate plane to show the relationship between x and y visually. Follow these steps to graph the equation \( y = 17x + 138 \):

- Identify the y-intercept (b), which is 138 in this equation. Plot this point on the y-axis at (0, 138).
- Use the slope (m) to find another point. Here, the slope is 17, which means for every 1 unit you move right, move up 17 units.
- Draw a straight line through these points to complete the graph.
Graphing helps visualize how changes in the variable x affect the variable y. It's a powerful tool to understand linear relationships better.
algebraic substitution
Algebraic substitution is a method used to solve equations by replacing variables with their values. To find the y-intercept of the equation \( y = 17x + 138 \), you need to substitute specific values.

Here's how it works:
  • Substitute x with 0 because the y-intercept always occurs at \( x=0 \).
  • Replace x in the equation with 0, then solve for y: \( y = 17(0) + 138 \).
  • Simplify the equation to find \( y \): \( y = 138 \).
In this example, the y-intercept is 138. Substitution is a basic yet essential algebraic technique that helps to find specific values in equations easily.

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Most popular questions from this chapter

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