/*! 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 264 In the following exercises, grap... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 11: Problem 264

In the following exercises, graph the line given a point and the slope. $$ (-4,2) ; m=4 $$

Short Answer

Expert verified
Equation: \( y = 4x + 18 \); Plot points \((-4, 2)\) and \((-3, 6)\); Draw line.

Step by step solution

01

Understand the Point-Slope Formula

The point-slope formula for the equation of a line is given by \[ y - y_1 = m(x - x_1) \] where \( (x_1, y_1) \) is a point on the line and \( m \) is the slope of the line.
02

Substitute Point and Slope into the Formula

Substitute the given point \( (-4, 2) \) and the given slope \( m = 4 \) into the point-slope form of the equation: \[ y - 2 = 4(x + 4) \]
03

Simplify the Equation

Distribute the slope and simplify the equation: \[ y - 2 = 4x + 16 \] \[ y = 4x + 18 \]
04

Plot the Point

On a graph, plot the given point \((-4, 2)\).
05

Use the Slope to Find Another Point

From the point \((-4, 2)\), use the slope \( m = 4 \). Since the slope means 'rise over run', go up 4 units and 1 unit to the right to find another point, \((-3, 6)\).
06

Draw the Line

Draw a straight line through the points \((-4, 2)\) and \((-3, 6)\). This is the graph of the equation \( y = 4x + 18 \).

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.

Point-Slope Formula
The point-slope formula is key to writing the equation of a line when you know a point on the line and its slope. This formula is expressed as \[ y - y_1 = m(x - x_1) \]. Here, \( (x_1, y_1) \) represents any point on the line, and \( m \) is the slope. It allows you to capture all possible y-values based on the x-values and the given slope.
Suppose we know that a line passes through the point \( (-4, 2) \) and has a slope \( m = 4 \). Plugging these values into the point-slope formula, we get: \[ y - 2 = 4(x + 4) \]. This represents the equation of our line.
Plotting Points
Plotting points is integral to graphing linear equations. A point is denoted as \( (x, y) \) where \( x \) indicates the horizontal position and \( y \) the vertical position on a graph.
First, plot the given point \( (-4, 2) \). Start at the origin \( (0, 0) \), then move 4 units to the left for the x-coordinate (-4), and 2 units up for the y-coordinate (2). Mark this point.
Once you have your starting point, use the slope to plot another point.
Calculating Slope
Slope measures the steepness of a line and is calculated as the 'rise over run', which means \( \text{slope} = \frac{\text{change in } y}{\text{change in } x} \). For the given slope \( m = 4 \), this means for every 1 unit you move horizontally to the right, you move 4 units vertically up.
From the point \( (-4, 2) \), move 1 unit right to \( -3 \) and 4 units up to \( 6 \). This gives another point \( (-3, 6) \) on your line.
Finally, use a ruler to draw a straight line through the two points. This line represents the equation \( y = 4x + 18 \).
Understanding how to calculate slope simplifies graphing linear equations and enhances interpreting and predicting data.

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 three solutions to each equation and then graph each line. $$ y=-3 x $$

In the following exercises, find the intercepts. $$ y=\frac{1}{4} x-1 $$

In the following exercises, find the intercepts. $$ x+2 y=10 $$

In the following exercises, for each ordered pair, decide a. if the ordered pair is a solution to the equation. b. if the point is on the line. \(y=\frac{2}{3} x-1\) (a) \((0,-1)\) (b) \((3,1)\) (c) \((-3,-3)\) (d) \((6,4)\)

In the following exercises, graph the vertical or horizontal lines. $$ y=-2 $$
See all solutions

Recommended explanations on Math Textbooks

Statistics

Read Explanation

Discrete Mathematics

Read Explanation

Pure Maths

Read Explanation

Logic and Functions

Read Explanation

Geometry

Read Explanation

Mechanics Maths

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.