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Chapter 11: Problem 307

In the following exercises, find the intercepts. $$ y=3 x $$

Short Answer

Expert verified
Both intercepts are at (0, 0).

Step by step solution

01

- Find the y-intercept

The y-intercept is the value of y when x is 0. Substitute x=0 into the equation: \[ y = 3(0) \]Thus, y = 0. The y-intercept is (0, 0).
02

- Find the x-intercept

The x-intercept is the value of x when y is 0. Substitute y=0 into the equation: \[ 0 = 3x \]Solving for x, we get x = 0. The x-intercept is (0, 0).

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Key Concepts

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

Understanding the y-intercept
The y-intercept of a linear equation is where the line crosses the y-axis. This means it is the point where the value of x is zero. Finding the y-intercept helps us understand how the line behaves when it starts off.
To determine the y-intercept, we set x to 0 in the equation. For example, in the equation \(y = 3x\), we substitute x = 0, which gives us: \[ y = 3(0) = 0 \] Thus, the y-intercept is the point (0, 0).
In summary:
  • Identify the y-intercept by setting x to 0.li>
  • The y-intercept tells us the starting point of our line on the y-axis.
Understanding the x-intercept
The x-intercept of a linear equation is where the line crosses the x-axis. This point is crucial because it shows the value of x when y is zero.
To find the x-intercept, we set y to 0 in the equation. Let's use the same example, \(y = 3x\). Setting y = 0, we get: \[0 = 3x\] We solve for x, finding that x = 0. Therefore, the x-intercept is also the point (0, 0).
In summary:
  • Identify the x-intercept by setting y to 0.
  • The x-intercept shows where the line meets the x-axis.
Introduction to Linear Equations
Linear equations are equations of the first order. This means they graph as straight lines in the coordinate plane. A common form is \[y = mx + b\] where:
  • m is the slope, indicating the steepness of the line.
  • b is the y-intercept, showing where the line crosses the y-axis.

Understanding linear equations helps us create and interpret graphs. They are foundational in algebra and appear in various real-world situations, such as calculating distances, budgeting, and predicting trends.
To solve linear equations:
  • Find the y-intercept by setting x to 0.
  • Find the x-intercept by setting y to 0.
  • Use the slope (m) to determine how steep the line is.

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Most popular questions from this chapter

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