Question

Graph the given equation. $$ y=-\frac{1}{2} x+3 $$

   Graph the given equation. 
$$
y=-\frac{1}{2} x+3
$$

Finite Mathematics and Applied Calculus

Finite Mathematics and Applied Calculus

Stefan Waner, Steven… 5th Edition

Chapter 1, Problem 28

Instant Answer

Solved by Expert Gregory Higby

09/23/2021

Step 1

The equation is in the form of $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept. In this case, $m = -\frac{1}{2}$ and $b = 3$. Show more…

Show all steps

lock

Thanks for your feedback!

Graph the given equation. $$ y=-\frac{1}{2} x+3 $$

Play audio

Feedback

Powered by NumerAI

Gregory Higby and 94 other subject Algebra educators are ready to help you.

Ask a new question

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Graphing Linear Equations

Graphing linear equations involves plotting the y-intercept on the coordinate plane and then using the slope to determine another point on the line. Once two points are identified, a straight line is drawn through them, representing the set of all solutions to the equation.

Linear Equation

A linear equation is an algebraic equation in which each term is either a constant or the product of a constant and a single variable. Linear equations graph as straight lines on the coordinate plane, and understanding their structure is fundamental to analyzing relationships between variables.

Slope-Intercept Form

The slope-intercept form of a linear equation is written as y = mx + b, where 'm' represents the slope of the line and 'b' represents the y-intercept. This form is particularly useful for graphing because it directly shows how steep the line is and where it crosses the y-axis.

Slope

The slope is a measure of the steepness of a line and indicates how much the y-value of a point on the line changes for a unit change in the x-value. It is calculated as the ratio of the vertical change to the horizontal change between two distinct points on the line.

Y-intercept

The y-intercept is the point at which a line crosses the y-axis, which occurs when the value of x is zero. It provides a starting point for graphing the linear equation and helps in understanding the behavior of the line on the coordinate plane.

Recommended Videos

Transcript

Ace is your personal tutor. It breaks down any question with clear steps so you can learn.

Start Using Ace

Continue solving this problem

Create a free account to:

View full step-by-step solution
Ask follow-up questions with Ace AI
Save progress and study later