Get started for free
Log In Start studying!
Get started for free Log out
Chapter 1: Problem 52
Use the y-intercept and slope to sketch the graph of each equation. $$y=-\frac{3}{2} x$$
Short Answer
Expert verified
The y-intercept is 0 and the slope is -\(\frac{3}{2}\). Plot (0,0) and (2,-3), then draw the line.
Step by step solution
01
Identify the slope
The given equation is \(y = -\frac{3}{2}x\). The slope, which is the coefficient of \(x\), is \(-\frac{3}{2}\).
02
Identify the y-intercept
The equation \(y = -\frac{3}{2}x\) can be written as \(y = -\frac{3}{2}x + 0\). Thus, the y-intercept is 0.
03
Plot the y-intercept
Plot the y-intercept (0, 0) on the graph.
04
Use the slope to find another point
The slope \(-\frac{3}{2}\) means that for every 2 units you move to the right along the x-axis, you move down 3 units along the y-axis. Starting from the y-intercept (0, 0), move 2 units to the right and drop 3 units to plot the point (2, -3).
05
Draw the line
Draw a straight line passing through the points (0, 0) and (2, -3). This is the graph of the equation \(y = -\frac{3}{2}x\).
Key Concepts
These are the key concepts you need to understand to accurately answer the question.
Understanding the y-intercept
In the given equation, we have \(y = -\frac{3}{2}x\). To find the y-intercept, we need to consider where the line crosses the y-axis. The y-axis is where \(x = 0\). When we rewrite the equation as \(y = -\frac{3}{2}x + 0\), we can see that the y-intercept is \(0\). This tells us that the line intersects the y-axis at the point \((0, 0)\).
This point is very important when starting to sketch the graph since it gives us a fixed point to draw from.
Grasping the slope
In the equation \(y = -\frac{3}{2}x\), the slope of the line is the coefficient of \(x\), which is \(-\frac{3}{2}\). The slope indicates how steep the line is and in which direction it moves. A slope of \(-\frac{3}{2}\) tells us that for every 2 units we move to the right along the x-axis, we move down 3 units along the y-axis.
To break it down:
- A negative sign means the line goes downwards.
- The number \(\frac{3}{2}\) tells us the exact rate of descent relative to horizontal movement.
Understanding the slope helps us determine other points on the line.
Plotting points on the graph
Now that we know the y-intercept and the slope, plotting points becomes straightforward. Start with the y-intercept, \((0, 0)\).
From this point, look at the slope \(-\frac{3}{2}\):
- Move 2 units right along the x-axis.
- Move 3 units down along the y-axis.
This brings us to the point \((2, -3)\).
Plot this point as well.
Finally, draw a straight line through \((0, 0)\) and \((2, -3)\). This line represents the equation \(y = - \frac{3}{2} x\). Knowing how to plot points and draw a line using the slope is key in graphing linear equations.
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
Recommended explanations on Math Textbooks
Logic and Functions
Read ExplanationDiscrete Mathematics
Read ExplanationCalculus
Read ExplanationDecision Maths
Read ExplanationMechanics Maths
Read ExplanationStatistics
Read ExplanationWhat do you think about this solution?
We value your feedback to improve our textbook solutions.
Study anywhere. Anytime. Across all devices.
Sign-up for free
This website uses cookies to improve your experience. We'll assume you're ok with this, but you can opt-out if you wish. Accept
Privacy & Cookies Policy
Privacy Overview
This website uses cookies to improve your experience while you navigate through the website. Out of these, the cookies that are categorized as necessary are stored on your browser as they are essential for the working of basic functionalities of the website. We also use third-party cookies that help us analyze and understand how you use this website. These cookies will be stored in your browser only with your consent. You also have the option to opt-out of these cookies. But opting out of some of these cookies may affect your browsing experience.
Always Enabled
Necessary cookies are absolutely essential for the website to function properly. This category only includes cookies that ensures basic functionalities and security features of the website. These cookies do not store any personal information.
Any cookies that may not be particularly necessary for the website to function and is used specifically to collect user personal data via analytics, ads, other embedded contents are termed as non-necessary cookies. It is mandatory to procure user consent prior to running these cookies on your website.