/*! 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 262 In the following exercises, grap... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 11: Problem 262

In the following exercises, graph the line given a point and the slope. $$ (-1,0) ; m=\frac{1}{5} $$

Short Answer

Expert verified
Plot \( (-1,0) \) and \( (4, 1) \), then draw a line through the points.

Step by step solution

01

- Understand the problem

You are given a point \( (-1, 0) \) and a slope \( m=\frac{1}{5} \). The task is to graph the line that passes through this point with the given slope.
02

- Plot the given point

Start by plotting the point \( (-1, 0) \) on the coordinate plane. This point is located at \(-1\) on the x-axis and \0\ on the y-axis.
03

- Use the slope to find another point

The slope \( m=\frac{1}{5} \) means that for every 5 units you move horizontally, you move 1 unit vertically. From the point \((-1, 0)\), move 5 units to the right (x = -1 + 5 = 4) and 1 unit up (y = 0 + 1 = 1). You now have a second point: \( (4, 1) \).
04

- Plot the second point

Plot the second point \( (4, 1) \) on the coordinate plane. This is located at \4\ on the x-axis and \1\ on the y-axis.
05

- Draw the line

Using a ruler, draw a line through the points \((-1, 0)\) and \((4, 1)\). This is the graph of the line with the given slope and point.

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.

coordinate plane
A coordinate plane is a two-dimensional surface where we can plot points, lines, and curves. It is defined by a horizontal axis, called the x-axis, and a vertical axis, called the y-axis. These axes intersect at a point called the origin, which has coordinates (0,0).
slope
The slope of a line, represented by the letter 'm', is a measure of how steep the line is. It is calculated as the ratio of the vertical change (rise) to the horizontal change (run) between any two points on the line. A positive slope means the line rises as it moves from left to right, while a negative slope means it falls.
plotting points
Plotting points on the coordinate plane involves locating points by their coordinates, which are written in the form (x, y). The x-coordinate indicates how far to move horizontally from the origin, and the y-coordinate indicates how far to move vertically. For example, a point (3, 2) is 3 units to the right of the origin and 2 units up.
linear equations
A linear equation is any equation that can be written in the form y = mx + b, where 'm' is the slope and 'b' is the y-intercept. The graph of a linear equation is a straight line. By knowing the slope and a point on the line, we can easily graph the equation.

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, use the slope formula to find the slope of the line between each pair of points. $$ (2,1),(4,5) $$

In the following exercises, graph the line given a point and the slope. $$ (2,-2) ; m=\frac{5}{2} $$

In the following exercises, graph each equation. $$ x=3 $$

In the following exercises, graph each equation. $$ y=-\frac{1}{2} x+3 $$

In the following exercises, graph each pair of equations in the same rectangular coordinate system. $$ y=2 x \text { and } y=2 $$
See all solutions

Recommended explanations on Math Textbooks

Logic and Functions

Read Explanation

Statistics

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Pure Maths

Read Explanation

Discrete Mathematics

Read Explanation

Probability and Statistics

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.