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Chapter 3: Problem 51

Graph each linear equation. \(-3 y=15\)

Short Answer

Expert verified
y = -5 is a horizontal line at y = -5.

Step by step solution

01

Isolate the variable y

Start by isolating the variable y in the given equation. Divide both sides of the equation by -3 to solve for y.
02

Simplify the equation

Divide both sides by -3:\[-3y = 15 \rightarrow y = \frac{15}{-3} = -5\]
03

Identify the type of line

Since the equation simplifies to \(y = -5\), it indicates a horizontal line with a y-coordinate of -5.
04

Plot the line on a graph

Draw a horizontal line on the graph that crosses the y-axis at \(y = -5\). This line will be parallel to the x-axis.

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Key Concepts

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

isolating variables
Isolating variables is an essential step in solving equations, especially linear equations. The goal is to get the variable by itself on one side of the equation. In our example, we started with \[-3y = 15\]. To isolate the variable y, we need to eliminate the -3 that is multiplied by y. We do this by performing the opposite operation of multiplication, which is division. Therefore, we divide both sides of the equation by -3, simplifying it to \[y = \frac{15}{-3} = -5\]. Now, y is isolated.
simplifying equations
Simplifying equations is another critical step in solving linear equations. After isolating the variable y by dividing both sides by -3, the equation becomes \[y = \frac{15}{-3}\]. Simplification involves reducing this fraction to its simplest form. In this case, 15 divided by -3 equals -5. So, the simplified form of the equation is \[y = -5\]. Simplification helps in making the equation more manageable and easier to graph. It's an essential skill to ensure accuracy in solving mathematics problems.
horizontal lines
A horizontal line in a graph represents an equation where y is constant. In our example, after simplification, we get \[y = -5\]. This equation tells us that y is always -5, regardless of the value of x. Hence, when you plot this on a graph, it forms a horizontal line that crosses the y-axis at -5.
Horizontal lines are parallel to the x-axis and have a slope of zero. Knowing how to identify and plot horizontal lines is important for graphing solutions accurately.
plotting graphs
Plotting graphs is the final step in visualizing the solution to an equation. For the equation \[y = -5\], we need to draw a horizontal line that crosses the y-axis at -5.
Here鈥檚 how you do it:
  • First, locate the point (0, -5) on the y-axis.
  • Next, draw a straight line horizontally from this point, ensuring it is parallel to the x-axis.
  • All points on this horizontal line will have y-coordinates of -5.


Plotting graphs helps in understanding the behavior of linear equations visually, making abstract mathematical concepts more concrete.

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Most popular questions from this chapter

Plot and label each point in a rectangular coordinate system. $$ (-3,0) $$

The maximum benefit for the heart from exercising occurs if the heart rate is in the target heart rate zone. The lower limit of this target zone can be approximated by the linear equation $$ y=-0.65 x+143 $$ where \(x\) represents age and \(y\) represents heartbeats per minute. (Source: The Gazette.) (a) Complete the table of values for this linear equation. (b) Write the data from the table of values as ordered pairs. (c) Make a scatter diagram of the data. Do the points lie in an approximately linear pattern?

Plot each set of points, and draw a line through them. Then give the equation of the line. $$ (3,5),(3,0), \text { and }(3,-3) $$

If two lines are both vertical or both horizontal, which of the following are they? A. Parallel B. Perpendicular C. Neither parallel nor perpendicular

Plot and label each point in a rectangular coordinate system. $$ (5,-4.25) $$
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