/*! 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 6 Find the coordinates of the poin... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 1: Problem 6

Find the coordinates of the points where the line $$ x-2 y=2 $$ intersects the axes. Hence sketch its graph.

Short Answer

Expert verified
The line intersects the axes at (2, 0) and (0, -1).

Step by step solution

01

Identify the Equation

The given line equation is: \[ x - 2y = 2 \]
02

Find the x-intercept

To find the x-intercept, set y = 0:\[ x - 2(0) = 2 \]Simplify:x = 2.So, the x-intercept is (2, 0).
03

Find the y-intercept

To find the y-intercept, set x = 0:\[ 0 - 2y = 2 \]Simplify:\[ y = -1 \].So, the y-intercept is (0, -1).
04

Plot the Points and Sketch the Graph

Plot the points (2, 0) and (0, -1) on the coordinate plane. Draw a straight line through these points to represent the line \[x - 2y = 2 \].

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
The x-intercept of a line is the point where the line crosses the x-axis. To find this point, we set the value of y to 0 in the line's equation because, on the x-axis, the y-coordinate of all points is 0. For example, let's consider the equation of the line provided: \[ x - 2y = 2 \]. To determine the x-intercept, set y = 0: \[ x - 2(0) = 2 \]. Simplifying this, we obtain: \[ x = 2 \]. Thus, the x-intercept is the point (2, 0). This means the line crosses the x-axis at the coordinate (2, 0). This process is significant since the x-intercept is a crucial point for fully understanding the behavior and position of the line on the graph.
y-intercept
The y-intercept of a line is the point where the line crosses the y-axis. This point is found by setting the value of x to 0 in the line's equation because, on the y-axis, the x-coordinate of all points is 0. Using the given line equation \[ x - 2y = 2 \], we can find the y-intercept by setting x = 0: \[ 0 - 2y = 2 \]. Simplifying this, we get: \[ -2y = 2 \rightarrow y = -1 \]. Thus, the y-intercept is the point (0, -1). This process is vital for graphing because knowing where the line intersects the y-axis helps in accurately plotting the line and understanding its vertical position regarding the origin.
graph sketching
Graph sketching involves plotting points and drawing the line that represents the equation. For the equation \[ x - 2y = 2 \], we have the x-intercept (2, 0) and the y-intercept (0, -1). To sketch the graph, follow these steps:
  • First, plot the x-intercept (2, 0) on the coordinate plane. This is the point where the line crosses the x-axis.
  • Next, plot the y-intercept (0, -1) on the coordinate plane. This is the point where the line crosses the y-axis.
  • Then, take a ruler and draw a straight line through these two points. This line represents the equation \[ x - 2y = 2 \].
Drawing a graph helps visualize the relationship between x and y values described by the equation. It shows the slope of the line and where it interacts with both axes.

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

Find expressions for the following algebraic fractions, simplifying your answers as far as possible. (a) \(\frac{5}{x-1} \times \frac{x-1}{x+2}\) (b) \(\frac{x^{2}}{x+10} \div \frac{x}{x+1}\) (c) \(\frac{4}{x+1}+\frac{1}{x+1}\) (d) \(\frac{2}{x+1}-\frac{1}{x+2}\)

Solve the following system of equations: $$ \begin{gathered} 2 x+2 y-5 z=-5 \\ x-y+z=3 \\ -3 x+y+2 z=-2 \end{gathered} $$

(Excel) Consider the consumption function $$ C=120+0.8 Y_{\mathrm{d}} $$ where \(Y_{\mathrm{d}}\) is disposable income. Write down expressions for \(C\), in terms of national income, \(Y\), when there is (a) no tax (b) a lump sum tax of \(\$ 100\) (c) a proportional tax in which the proportion is \(0.25\) Sketch all three functions on the same diagram, over the range \(0 \leq Y \leq 800\), and briefly describe any differences or similarities between them. Sketch the 45 degree line, \(C=Y\), on the same diagram, and hence estimate equilibrium levels of national income in each case.

(Excel) If the consumption function is $$ C=0.9 Y+20 $$ and planned investment \(I=10\), write down an expression for the aggregate expenditure, \(C+I\), in terms of \(Y\). Draw graphs of aggregate expenditure, and the 45 degree line, on the same diagram, over the range \(0 \leq Y \leq 500\). Deduce the equilibrium level of national income. Describe what happens to the aggregate expenditure line in the case when (a) the marginal propensity to consume falls to \(0.8\) (b) planned investment rises to 15 and find the new equilibrium income in each case.

The demand and supply functions for two interdependent commodities are given by $$ \begin{aligned} &Q_{\mathrm{D}_{1}}=100-2 P_{1}+P_{2} \\ &Q_{\mathrm{D}_{2}}=5+2 P_{1}-3 P_{2} \\ &Q_{\mathrm{S}_{1}}=-10+P_{1} \\ &Q_{\mathrm{s}_{2}}=-5+6 P_{2} \end{aligned} $$ where \(Q_{D_{i}}, Q_{s_{i}}\) and \(P_{i}\) denote the quantity demanded, quantity supplied and price of good \(i\) respectively. Determine the equilibrium price and quantity for this two-commodity model.
See all solutions

Recommended explanations on Math Textbooks

Probability and Statistics

Read Explanation

Calculus

Read Explanation

Discrete Mathematics

Read Explanation

Geometry

Read Explanation

Theoretical and Mathematical Physics

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.