Question content area top left
Part 1
Graph the equation on paper, and then choose the correct graph on the right.
y=
1
6x
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 is plotted. As x increases comma the curve rises from the point left parenthesis 0 comma 0 right parenthesis comma passes through the point left parenthesis 1 comma 1 right parenthesis comma and continues to rise toward infinity. As x increases comma the curve rises 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 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.
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 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.
D.
-5
5
-5
5
x
y
The correct graph for the equation y=1/6x is A
To graph the equation y = 1/6x, we need to plot points on a coordinate system and connect them to form a curve.
Step 1: Choose a set of x-values. Let's choose x = -6, -3, 0, 3, and 6.
Step 2: Substitute the chosen x-values into the equation to find the corresponding y-values.
When x = -6, y = (1/6)(-6) = -1
When x = -3, y = (1/6)(-3) = -1/2
When x = 0, y = (1/6)(0) = 0
When x = 3, y = (1/6)(3) = 1/2
When x = 6, y = (1/6)(6) = 1
Step 3: Plot the points (-6, -1), (-3, -1/2), (0, 0), (3, 1/2), and (6, 1) on a coordinate system.
Step 4: Connect the points with a smooth curve. The curve should rise from the point (0, 0) and pass through the points (1, 1/6) and (3, 1/2).
Now, let's choose the correct graph from the given options (A, B, C, D).
Based on the information provided, the correct graph for the equation y = 1/6x is Option A:
A.
-5
5
-5
5
x
y
This graph shows the curve rising from the point (0, 0) and passing through the points (1, 1/6) and (3, 1/2) as x increases.
To graph the equation y = 1/6x on paper, we will plot points on a coordinate system.
1. First, draw a coordinate system with a horizontal x-axis labeled from -5 to 5 in increments of 1 and a vertical y-axis labeled from -5 to 5 in increments of 1.
2. To plot points, substitute different values of x into the equation and solve for y. For example, let's substitute x = -5 into the equation:
y = 1/6(-5)
y = -5/6
So, the point (-5, -5/6) is plotted on the graph.
3. Repeat this process for other values of x, such as x = -4, x = -3, ..., x = 4, x = 5. Plot each point on the graph.
4. Connect the plotted points with a smooth curve. As x increases, the curve rises from the point (0,0), passes through (1,1), and continues to rise toward infinity. However, the curve rises more and more slowly as x increases.
Now, let's determine which graph among A, B, C, and D matches the graph we just plotted.
Option A describes the correct graph. It mentions that as x increases, the curve rises from (0,0), passes through (1,1), and continues to rise toward infinity, while rising more and more slowly.