/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 154 In the following exercises, find... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 11: Problem 154

In the following exercises, find the intercepts. $$ y=5 x $$

Short Answer

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

Step by step solution

01

- Find the x-intercept

To find the x-intercept, set y to 0 and solve for x. Starting with the equation: \[ y = 5x \] Set \( y = 0 \): \[ 0 = 5x \] Solving for x: \[ x = 0 \] So the x-intercept is at the point (0, 0).
02

- Find the y-intercept

To find the y-intercept, set x to 0 and solve for y. Starting with the equation: \[ y = 5x \] Set \( x = 0 \): \[ y = 5 \times 0 \] Solving for y: \[ y = 0 \] So the y-intercept is at the point (0, 0).

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

Key Concepts

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

x-intercept
To understand the x-intercept, imagine where a line crosses the x-axis. This point always has a value of 0 for y. In other words, to find the x-intercept in a linear equation like \( y = 5x \), we set y to 0 and solve for x. Plugging in 0 for y gives us \[ 0 = 5x \]. This simplifies to \[ x = 0 \]. Therefore, the x-intercept is at \( (0, 0) \). You can visualize this as the point where the line hits the x-axis.
y-intercept
The y-intercept is where our line touches the y-axis. At this point, x is always 0. To find the y-intercept in a linear equation like \( y = 5x \), we set x to 0 and solve for y. Doing so gives us \[ y = 5 \times 0 = 0 \]. Thus, the y-intercept is also at \( (0, 0) \). This means that for this particular equation, the line passes through the origin point \( (0, 0) \).
linear equations
Linear equations are mathematical expressions that describe straight lines. They generally take the form \( y = mx + b \), where 'm' is the slope and 'b' is the y-intercept. In the equation \( y = 5x \), the slope (m) is 5, and the y-intercept (b) is 0. Since there is no 'b' term in the equation, it means the line passes through the origin. Linear equations are simple yet powerful tools used to understand the relationship between two variables. They are foundational in algebra and help us understand various real-world phenomena such as speed, distance, and even economics.

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

In the following exercises, find the intercepts. $$ x-y=-1 $$

In the following exercises, graph each equation. $$ y=\frac{1}{4} x-2 $$

A bicycle route climbs 20 feet for 1,000 feet of horizontal distance. What is the slope of the route?

Plot and label these points: (a) \((2,5)\) (b) \((-1,-3)\) (c) \((-4,0)\) (d) \((3,-5)\) (e) \((-2,1)\)

In the following exercises, use the slope formula to find the slope of the line between each pair of points. $$ (-1,-1),(0,-5) $$
See all solutions

Recommended explanations on Math Textbooks

Calculus

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Probability and Statistics

Read Explanation

Mechanics Maths

Read Explanation

Decision Maths

Read Explanation

Logic and Functions

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.