Graph the equation on paper, and then choose the correct graph on the right.
y=
1
3x
Question content area bottom left
Part 1
Choose the correct graph.
.
.
.
Question content area right
Part 1
A.
-5
5
-5
5
x
y
A coordinate system has a horizontal x-axis labeled from negative 5 to 5 in increments of 1 and a vertical y-axis labeled from negative 5 to 5 in increments of 1. A curve has the x-axis as an asymptote. As x increases, the curve falls from infinity, passes through the point (0, 1), and continues to fall toward the x-axis. As x increases, the curve falls more and more slowly.
B.
-5
5
-5
5
x
y
A coordinate system has a horizontal x-axis labeled from negative 5 to 5 in increments of 1 and a vertical y-axis labeled from negative 5 to 5 in increments of 1. A curve has the x-axis as an asymptote. As x increases, the curve rises from just above the x-axis, passes through the point (0, 1), and continues to rise toward infinity. As x increases, the curve rises more and more quickly.
C.
-5
5
-5
5
x
y
A coordinate system has a horizontal x-axis labeled from negative 5 to 5 in increments of 1 and a vertical y-axis labeled from negative 5 to 5 in increments of 1. A curve has the y-axis as an asymptote. As x increases from 0, the curve falls from infinity, passes through the point (1, 0), and continues to fall toward negative infinity. As x increases, the curve falls more and more slowly.
D.
-5
5
-5
5
x
y
The correct graph for the equation y = 1/3x is Option D.
The correct graph is B.
A coordinate system has a horizontal x-axis labeled from negative 5 to 5 in increments of 1 and a vertical y-axis labeled from negative 5 to 5 in increments of 1. A curve has the x-axis as an asymptote. As x increases, the curve rises from just above the x-axis, passes through the point (0, 1), and continues to rise toward infinity. As x increases, the curve rises more and more quickly.
To graph the equation y = 1/3x, we can follow these steps:
1. Set up a coordinate system on a piece of graph paper with the x-axis labeled from -5 to 5 and the y-axis labeled from -5 to 5.
2. Plot the point (0, 1) on the graph. This is the point where the curve intersects the y-axis.
3. Determine other points on the graph by choosing different values of x. For example, you can choose x = -3, -2, -1, 1, 2, 3, and substitute these values into the equation to find the corresponding y-values.
4. Connect the plotted points with a smooth curve that passes through the plotted points.
Now, let's analyze the options provided:
Option A: This option describes a curve that falls from infinity as x increases and passes through the point (0, 1). This matches the behavior of the graph of y = 1/3x.
Option B: This option describes a curve that rises from just above the x-axis as x increases and passes through the point (0, 1). This does not match the behavior of the graph of y = 1/3x.
Option C: This option describes a curve that has the y-axis as an asymptote and falls towards negative infinity as x increases. This does not match the behavior of the graph of y = 1/3x.
Option D: This option does not provide any description of the graph.
Based on the analysis, the correct graph is Option A.