Graph The Equation $y=-\frac{1}{2} X+7$.Select Points On The Graph To Indicate Where The Line Passes Through.
Introduction
Graphing linear equations is a fundamental concept in mathematics that helps us visualize the relationship between two variables. In this article, we will focus on graphing the equation $y=-\frac{1}{2} x+7$. We will explore the steps involved in graphing this equation and select points on the graph to indicate where the line passes through.
Understanding the Equation
The given equation is in the slope-intercept form, which is $y=mx+b$, where $m$ is the slope and $b$ is the y-intercept. In this case, the slope is $-\frac{1}{2}$ and the y-intercept is $7$. The slope represents the rate of change of the line, and the y-intercept represents the point where the line intersects the y-axis.
Graphing the Equation
To graph the equation, we need to find two points on the line. We can do this by substituting different values of $x$ into the equation and solving for $y$. Let's start by finding the y-intercept, which is the point where $x=0$. Substituting $x=0$ into the equation, we get:
So, the y-intercept is $(0,7)$. This means that the line passes through the point $(0,7)$.
Next, let's find another point on the line. We can do this by substituting a value of $x$ into the equation and solving for $y$. Let's choose $x=4$. Substituting $x=4$ into the equation, we get:
So, the point $(4,6)$ is also on the line.
Plotting the Points
Now that we have two points on the line, we can plot them on a coordinate plane. The x-axis represents the horizontal axis, and the y-axis represents the vertical axis. We can plot the points $(0,7)$ and $(4,6)$ on the coordinate plane.
Drawing the Line
Once we have plotted the two points, we can draw a line through them to represent the graph of the equation. The line should be a straight line that passes through the two points.
Selecting Points on the Graph
To select points on the graph, we need to find the coordinates of the points where the line passes through. We can do this by substituting different values of $x$ into the equation and solving for $y$. Let's choose some values of $x$ and find the corresponding values of $y$.
| $x$ | $y$ |
|---|---|
| 0 | 7 |
| 4 | 6 |
| 8 | 5 |
| 12 | 4 |
| 16 | 3 |
We can plot these points on the coordinate plane and draw a line through them to represent the graph of the equation.
Conclusion
Introduction
Graphing linear equations is a fundamental concept in mathematics that helps us visualize the relationship between two variables. In our previous article, we graphed the equation $y=-\frac{1}{2} x+7$ and selected points on the graph to indicate where the line passes through. In this article, we will answer some frequently asked questions about graphing linear equations.
Q&A
Q: What is the slope-intercept form of a linear equation?
A: The slope-intercept form of a linear equation is $y=mx+b$, where $m$ is the slope and $b$ is the y-intercept.
Q: What is the slope of a linear equation?
A: The slope of a linear equation is the rate of change of the line. It represents how much the line rises or falls as we move along the x-axis.
Q: What is the y-intercept of a linear equation?
A: The y-intercept of a linear equation is the point where the line intersects the y-axis. It represents the value of $y$ when $x=0$.
Q: How do I graph a linear equation?
A: To graph a linear equation, you need to find two points on the line. You can do this by substituting different values of $x$ into the equation and solving for $y$. Once you have two points, you can plot them on a coordinate plane and draw a line through them to represent the graph of the equation.
Q: How do I select points on the graph of a linear equation?
A: To select points on the graph of a linear equation, you need to substitute different values of $x$ into the equation and solve for $y$. You can then plot these points on the coordinate plane and draw a line through them to represent the graph of the equation.
Q: What is the difference between a linear equation and a quadratic equation?
A: A linear equation is an equation in which the highest power of the variable is 1. A quadratic equation is an equation in which the highest power of the variable is 2.
Q: How do I graph a linear equation with a negative slope?
A: To graph a linear equation with a negative slope, you need to find two points on the line. You can do this by substituting different values of $x$ into the equation and solving for $y$. Once you have two points, you can plot them on a coordinate plane and draw a line through them to represent the graph of the equation. The line will slope downward from left to right.
Q: How do I graph a linear equation with a positive slope?
A: To graph a linear equation with a positive slope, you need to find two points on the line. You can do this by substituting different values of $x$ into the equation and solving for $y$. Once you have two points, you can plot them on a coordinate plane and draw a line through them to represent the graph of the equation. The line will slope upward from left to right.
Conclusion
Graphing linear equations is an important concept in mathematics that helps us visualize the relationship between two variables. In this article, we answered some frequently asked questions about graphing linear equations. We hope that this article has been helpful in clarifying any confusion you may have had about graphing linear equations.
Additional Resources
If you are looking for additional resources to help you learn about graphing linear equations, here are a few suggestions:
- Khan Academy: Graphing Linear Equations
- Mathway: Graphing Linear Equations
- Wolfram Alpha: Graphing Linear Equations
We hope that these resources are helpful in your learning journey.