/*! 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 18 Graph each equation by finding t... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 5: Problem 18

Graph each equation by finding the intercepts and at least ne ether point. $$5 x+y=10$$

Short Answer

Expert verified
The line representing the equation \(5x + y = 10\) can be graphed by finding the x-intercept (2, 0), y-intercept (0, 10), and another point (1, 5). Plot these points and draw a straight line through them, extending it through the entire graph.

Step by step solution

01

Find the x-intercept

To find the x-intercept, set y = 0 in the given equation: \(5x + 0 = 10\) Solve for x: \(5x = 10\) \(x = \dfrac{10}{5}\) \(x = 2\) So, the x-intercept is the point (2, 0).
02

Find the y-intercept

To find the y-intercept, set x = 0 in the given equation: \(5(0) + y = 10\) Solve for y: \(y = 10\) So, the y-intercept is the point (0, 10).
03

Find another point on the line

To find another point on the line, we can substitute any value for x (other than the x-intercept) into the equation and solve for y. Let's use x = 1: \(5(1) + y = 10\) Solve for y: \(5 + y = 10\) \(y = 10 - 5\) \(y = 5\) So, another point on the line is (1, 5).
04

Graph the line

By plotting the points found in steps 1 through 3, we can draw the line representing the given equation. The points are (2, 0), (0, 10), and (1, 5). Once these points are plotted, draw a straight line through them, extending this line through the entire graph. This line now represents the equation \(5x + y = 10\).

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.

Intercepts
In graphing linear equations, intercepts are crucial because they provide points where the line crosses the axes. The x-intercept is where the line crosses the x-axis. To find this point, set the y-value to zero in the equation. For example, with the equation given, when we set \( y = 0 \), we solve for \( x \) which yields the x-intercept (2, 0).
Similarly, the y-intercept is found by setting the x-value to zero and solving for \( y \). This gives us the point (0, 10) for the y-intercept in the equation \( 5x + y = 10 \).
Intercepts help in giving a starting point for drawing the graph of the line, as these are points through which the line must pass.
Equation of a Line
The equation \( 5x + y = 10 \) is a linear equation which forms a straight line when graphed. The general form for a line equation is \( Ax + By = C \), where A, B, and C are constants. This formula represents a straight line. It includes both x and y variables that describe a series of infinite points laid out in a straight path.
The equation effectively tells us how x and y relate across that line. By manipulating this equation, such as rearranging to \( y = mx + c \), you can derive slope-intercept form where \( m \) is the slope and \( c \) is the y-intercept. Understanding this form is essential for easily identifying the slope and where the line crosses the y-axis.
Coordinate Points
Coordinate points are essential in graphing because they represent precise locations on a graph. Each point is defined by a pair of values (x, y), indicating the position on the Cartesian plane.
In the context of our linear equation, important points were found: \((2, 0)\), \((0, 10)\), and \((1, 5)\). Each point plays a role in constructing the overall picture of the line.
By using the equation to find these points, we can ensure that points lie on the line and accurately represent the equation's solution set. Plotting them on the graph and connecting them forms the visual representation of the equation, making these points vital for correctly drawing a line.

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

Solve each systen \(3 x+4 y=-6\) \(-x+3 z=1\) \(2 y+3 z=-1\)

Write a system of equations and solve. A movie theater charges \(\$ 9.00\) for an adult's ticket. S7. OO for a ticket for scriors 60 and over, and \(\$ 6,00\) for a child's ticket. For a particular movie, the theater sold a total of 290 tickets. which brought in \(\$ 2400\). The number of semors' 'tickets sold was twice the number of children's tickets sold. Determine the number of ndults", scniors', and children's tickets sold.

Determine the domain of each relation, and determine whether each relation describes \(y\) as a function of \(x .\) $$y=\frac{15}{x}$$

The measure of the largest angle of a triangle is twice the middle angle. The smallest angle measures \(28^{\circ}\) less than the middle angle. Find the measures of the angles of the triangle. (Hint: Recall that the sum of the measures of the angles of a triangle is \(180^{\circ}\).)

For each function, \(f,\) find \(f(3)\) and \(f(-2)\) Graph \(f(x)=-2 x+6\) by making a table of values and plotting points.
See all solutions

Recommended explanations on Math Textbooks

Geometry

Read Explanation

Calculus

Read Explanation

Discrete Mathematics

Read Explanation

Mechanics Maths

Read Explanation

Statistics

Read Explanation

Pure 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.