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Chapter 7: Problem 43

Graph each horizontal or vertical line. \(y=-2\)

Short Answer

Expert verified
The line graph for the equation \(y = -2\) is a horizontal line passing through the point (0, -2)

Step by step solution

01

Understand the Line

The equation given is \(y = -2\). This refers to a horizontal line, where every point along the line has an y-coordinate of -2, no matter what its x-coordinate is.
02

Drawing the Line

Begin at the origin of your graph. Move two units down along the y-axis. This is the location of the horizontal line. Now draw a straight line going through this point, that extends across the entire graph horizontally.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Horizontal Line Equation
Understanding the equation of a horizontal line is fundamental in coordinate geometry. Such an equation has the form y = c, where c is a constant. This means that no matter what the value of x is, the value of y will always be c. It's a straight line parallel to the x-axis, and its distance from the x-axis is determined by the value of c. For example, in the equation y = -2, the line runs horizontally and crosses the y-axis at -2.
  • All points on this line have a y-coordinate of -2.
  • The slope of a horizontal line is 0, which means that it does not rise or fall as it moves from left to right.
  • It's independent of x, therefore the x-coordinate could be any real number.
Remembering this pattern makes it straightforward to identify horizontal lines on a graph and understand their behavior.
Plotting Graphs
To effectively translate equations into visual representations, it's important to know how to plot graphs. Graphs help us visualize mathematical concepts and find solutions to complex problems. Here are the steps to graph a horizontal line like y = -2:
  • Start with a Cartesian coordinate system. Draw a horizontal x-axis and a vertical y-axis, intersecting at the origin (0,0).
  • Locate the y-value given in the equation along the y-axis. For y = -2, mark the point (0, -2).
  • Since it's a horizontal line, you'll want to draw a line parallel to the x-axis, passing through (0, -2), extending to the left and right edges of your graph.
  • Use a ruler for a perfectly straight line, to accurately represent the equation.
Plotting graphs correctly allows you to see patterns, make predictions, and better understand the relationship between variables.
Coordinate Geometry
Coordinate geometry, also known as analytic geometry, is the study of geometric figures through the use of coordinates on graphs. It combines algebra and geometry to solve problems involving lines, curves, and shapes.
  • Coordinate geometry deals with points defined by coordinates, usually in pairs for two-dimensional spaces: the x (horizontal) and y (vertical) coordinates.
  • It can be used to determine the slope, distance between points, and the equations of shapes.
  • In the context of horizontal lines, coordinate geometry helps us understand that the y-coordinate is fixed, while the x-coordinate can vary freely. This is seen in the equation y = -2, which is plotted on a graph as a straight horizontal line.
Understanding coordinate geometry is crucial for graphing because it provides the tools necessary to translate equations into graphical representations, which can be analyzed and applied to real-world contexts.

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Most popular questions from this chapter

In Exercises 15-22, a. Create a scatter plot for the data in each table. b. Use the shape of the scatter plot to determine if the data are best modeled by a linear function, an exponential function, a logarithmic function, or a quadratic function. $$ \begin{array}{|c|c|} \hline \boldsymbol{x} & \boldsymbol{y} \\ \hline 0 & 0 \\ \hline 9 & 1 \\ \hline 16 & 1.2 \\ \hline 19 & 1.3 \\ \hline 25 & 1.4 \\ \hline \end{array} $$

Graph the solution set of each system of inequalities. \(\left\\{\begin{array}{l}x \geq 2 \\ y \leq 3\end{array}\right.\)

Graph the solution set of each system of inequalities. \(\left\\{\begin{array}{l}y>2 x-3 \\ y<-x+6\end{array}\right.\)

You are about to take a test that contains computation problems worth 6 points each and word problems worth 10 points each. You can do a computation problem in 2 minutes and a word problem in 4 minutes. You have 40 minutes to take the test and may answer no more than 12 problems. Assuming you answer all the problems attempted correctly, how many of each type of problem must you answer to maximize your score? What is the maximum score?

Use a table of coordinates to graph each exponential function. Begin by selecting \(-2,-1,0,1\), and 2 for \(x\). \(f(x)=3^{x-1}\)
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