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Chapter 3: Problem 65

Concept Check Plot each set of points, and draw a line through them. Then give the equation of the line. $$ (-3,-3),(0,-3), \text { and }(4,-3) $$

Short Answer

Expert verified
y = -3

Step by step solution

01

Identify the coordinates

Identify the given points: (-3, -3), (0, -3), and (4, -3).
02

Plot the points

Plot the points on the Cartesian plane: (-3, -3), (0, -3), and (4, -3).
03

Draw the line

Draw a straight line passing through all the plotted points.
04

Determine the nature of the line

Notice that all the points have the same y-coordinate, which means the line is horizontal.
05

Write the equation of the line

For a horizontal line, the equation is of the form y = c, where c is the y-coordinate of all points. Here, c = -3.

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Key Concepts

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

Plotting Points
Plotting points on a graph involves placing dots at specific coordinates on the Cartesian plane. Each point has an x-coordinate (how far along the x-axis) and a y-coordinate (how far up or down the y-axis). The coordinates are written in parentheses like this: (x, y).
For example, in the exercise, we had three points: (-3, -3), (0, -3), and (4, -3).
To plot these:
  • Start from the origin (0,0).
  • Move left or right to the x-coordinate value.
  • Then move up or down to the y-coordinate value.
  • Place a dot at the final position.
Cartesian Plane
The Cartesian plane consists of two perpendicular lines called axes.
The horizontal axis is called the x-axis, and the vertical axis is called the y-axis. These axes divide the plane into four quadrants.
Each point on the plane is defined by a pair of coordinates (x, y). The origin, where the x-axis and y-axis cross, has coordinates (0,0).
We used the Cartesian plane to plot points and draw lines in the exercise.
  • The x values tell us the horizontal position.
  • The y values tell us the vertical position.
Horizontal Line Equation
A horizontal line is a line that runs left to right and has a constant y-coordinate.
In the given exercise, all points shared the same y-coordinate (-3), meaning the line is horizontal.
The equation for a horizontal line is simple. It's always in the form y = c, where c is the y-coordinate of any point on the line.
For our example, the equation is y = -3 because all points had y-values of -3.
Linear Equations
Linear equations represent straight lines on a graph. They are usually written in the form y = mx + b, where:
  • m is the slope of the line.
  • b is the y-intercept, the y-coordinate where the line crosses the y-axis.

In some cases, such as with horizontal lines, the equation simplifies. For horizontal lines, the slope (m) is 0, so the equation simplifies to y = b.
The linear equation of the horizontal line through (-3, -3), (0, -3), and (4, -3) is y = -3. Always notice patterns in coordinates to determine the type of line.

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Most popular questions from this chapter

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