Explanations 
Textbooks 
Flashcards 
91影视 AI 
Notes 
Study Plans 
Study Sets 
Find a degree 
Magazine Chapter 1: Problem 31
Graph each line by hand. Give the \(x\) - and y-intercepts. $$2 x+5 y=10$$
Short Answer
Expert verified
x-intercept: (5, 0), y-intercept: (0, 2)
Step by step solution
01
Find the y-intercept
To find the y-intercept, set \(x = 0\) in the equation. The equation is \(2 \cdot 0 + 5y = 10\), which simplifies to \(5y = 10\). Solving for \(y\), we divide both sides by 5 to get \(y = 2\). Thus, the y-intercept is at the point \((0, 2)\).
02
Find the x-intercept
To find the x-intercept, set \(y = 0\) in the equation. The equation becomes \(2x + 5 \cdot 0 = 10\), simplifying to \(2x = 10\). Solving for \(x\), we divide both sides by 2 to get \(x = 5\). Thus, the x-intercept is at the point \((5, 0)\).
03
Plot the intercepts
On a coordinate plane, plot the points \((0, 2)\) and \((5, 0)\) that represent the y-intercept and the x-intercept respectively. These points will help you draw the line.
04
Draw the line
Using a ruler, draw a straight line through the points \((0, 2)\) and \((5, 0)\). Extend the line across the graph to show its path in both directions. This line represents the equation \(2x + 5y = 10\).
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.
X-intercept
In mathematics, the x-intercept is the point where a graph crosses the x-axis. This means that at this point, the value of y is zero. To find the x-intercept from a linear equation like the one given, you'll need to set y to zero and solve for x.
Let's look at the equation provided:
Let's look at the equation provided:
- Equation: \(2x + 5y = 10\)
- Set \( y = 0 \): \( 2x + 5 \cdot 0 = 10 \)
- This simplifies to \( 2x = 10 \)
- Solving for \( x \), divide both sides by 2, yielding \( x = 5 \)
Y-intercept
The y-intercept is another crucial point on a graph. It is where the line crosses the y-axis. At this interception, the value of x is zero. To find the y-intercept, you need to substitute x with zero in the linear equation and then solve for y.
Let's solve for the y-intercept in our example:
Let's solve for the y-intercept in our example:
- Equation: \(2x + 5y = 10\)
- Set \( x = 0 \): \( 2 \cdot 0 + 5y = 10 \)
- This simplifies to \( 5y = 10 \)
- Solving for \( y \) involves dividing both sides by 5, resulting in \( y = 2 \)
Coordinate Plane
The coordinate plane is a two-dimensional surface on which we can graph equations. It is composed of two axes鈥� the x-axis and the y-axis. These axes divide the plane into four quadrants, allowing us to pinpoint any location with precision.
Here鈥檚 what makes up the coordinate plane:
Here鈥檚 what makes up the coordinate plane:
- The horizontal line is the x-axis.
- The vertical line is the y-axis.
- The point where these two lines intersect is called the origin, denoted as (0,0).
Straight Line
A straight line is the simplest form of linear equations representation on a graph. It shows the constant relationship between two variables. On a coordinate plane, a line can be easily drawn if we know at least two points it passes through, like the x-intercept and y-intercept.
Steps to graph a straight line:
Steps to graph a straight line:
- Identify intercepts or any two points on the line.
- Plot these points on the coordinate plane.
- Use a ruler to draw a line through these points, extending it across the plane.
