/*! 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 50 Find the intercepts. Then graph.... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 3: Problem 50

Find the intercepts. Then graph. $$ 6 x+2 y=12 $$

Short Answer

Expert verified
x-intercept: (2, 0); y-intercept: (0, 6).

Step by step solution

01

- Find the x-intercept

To find the x-intercept, set y to 0. Solve for x in the equation \(6x + 2(0) = 12\). This simplifies to \(6x = 12\), giving \(x = 2\). Hence, the x-intercept is (2, 0).
02

- Find the y-intercept

To find the y-intercept, set x to 0. Solve for y in the equation \(6(0) + 2y = 12\). This simplifies to \(2y = 12\), giving \(y = 6\). Hence, the y-intercept is (0, 6).
03

- Plot the intercepts on a graph

To graph the equation, plot the intercepts \(2, 0\) and \(0, 6\) on the coordinate plane. Draw a straight line through these two points to represent the line \(6x + 2y = 12\).

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 is where a graph crosses the x-axis, so the coordinate for y will always be 0. To find the x-intercept of an equation, you simply substitute y with 0 and solve for x. For example, in the equation \(6x + 2y = 12\), replacing y with 0 gives \(6x + 2(0) = 12\). This simplifies to \(6x = 12\). Solving for x, we find \(x = 2\). Therefore, the x-intercept is at the point (2, 0).

Remember:
  • Set y to 0
  • Solve for x
  • The result is your x-intercept
y-intercept
The y-intercept is where a graph crosses the y-axis, meaning the coordinate for x will always be 0. To find the y-intercept, you set x to 0 and solve for y. Taking the equation \(6x + 2y = 12\) again, substituting x with 0 results in \(6(0) + 2y = 12\). This simplifies to \(2y = 12\). Solving for y, we get \(y = 6\). Hence, the y-intercept is at the point (0, 6).

Remember:
  • Set x to 0
  • Solve for y
  • The result is your y-intercept
graphing linear equations
Graphing linear equations involves plotting points on a coordinate plane and connecting them with a straight line. For the equation \(6x + 2y = 12\), first find the intercepts. We found the x-intercept to be (2, 0) and the y-intercept to be (0, 6). Next, we plot these points on the coordinate plane.

To complete the graph, draw a straight line through these two points. This line represents the equation \(6x + 2y = 12\). Since it is a linear equation, its graph will always be a straight line.

Remember:
  • Find intercepts
  • Plot points
  • Draw line through points
coordinate plane
The coordinate plane is a two-dimensional plane formed by the intersection of a vertical y-axis and a horizontal x-axis. Each point on this plane is defined by an ordered pair (x, y), where x is the horizontal coordinate and y is the vertical one.

For example, the point (2, 0) signifies 2 units along the x-axis and 0 units along the y-axis. Similarly, the point (0, 6) represents 0 units along the x-axis and 6 units up the y-axis. These points help in locating where a line or curve will pass.

The coordinate plane is fundamental in graphing equations and understanding the spatial relationship between variables.

Quick tips:
  • The x-axis is horizontal
  • The y-axis is vertical
  • Points are written as (x, y)
solving for intercepts
Solving for intercepts involves a straightforward method of isolating the variable.

To find the x-intercept, set y to 0 and solve the resulting equation for x.
To find the y-intercept, set x to 0 and solve the resulting equation for y.

Let's recap using the equation \(6x + 2y = 12\):
  • x-intercept: Set y = 0, then solve \(6x = 12\) to get x = 2.
  • y-intercept: Set x = 0, then solve \(2y = 12\) to get y = 6.
By following these steps, you can accurately determine both intercepts, making it easier to graph the equation on the coordinate plane.

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

For the function given by \(n(z)=a b+w z,\) what is the independent variable? How can you tell?

To prepare for Section \(3.7,\) review solving a formula for \(a\) variable and subtracting real numbers (Sections 1.6 and 2.3 ). Simplify. $$-10-(-3)$$

Assume that \(r, p,\) and \(s\) are constants and that \(x\) and \(y\) are variables. Determine the slope and the y-intercept. $$r x+p y=s-r y$$

Find the indicated function values for each function. $$F(x)=\left\\{\begin{array}{ll} {2 x,} & {\text { if } x \leq 0} \\ {x,} & {\text { if } 03} \end{array}\right.$$ a) \(F(-1)\) b) \(F(3)\) c) \(F(10)\)

Pressure at Sea Depth. The pressure \(P(d),\) in atmospheres, at a depth \(d\) feet beneath the surface of the ocean is given by \(P(d)=0.03 d+1\). a) What do the numbers 0.03 and 1 signify? b) Where is the pressure 4 atmospheres? c) What is the domain of \(P ?\)
See all solutions

Recommended explanations on Math Textbooks

Applied Mathematics

Read Explanation

Probability and Statistics

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Pure Maths

Read Explanation

Geometry

Read Explanation

Calculus

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.