Question content area top left
Part 1
Graph the equation on paper, and then choose the correct graph.
y=2x
Question content area bottom left
Part 1
Choose the correct graph on the right.
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Question content area right
Part 1
A.
-5
5
-5
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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 horizontal axis, passes through the point (0, 1), and continues to rise toward infinity. As x increases, the curve rises more and more quickly.
B.
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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 line that rises from left to right has slope 2 and crosses the vertical axis at the point (0, 1).
C.
-5
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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 falls from infinity comma passes through the point left parenthesis negative 1 comma 2 right parenthesis comma passes through its lowest point left parenthesis 0 comma 1 right parenthesis comma rises to pass through the point left parenthesis 1 comma 2 right parenthesis comma and continues to rise toward infinity.
D.
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y
The correct graph for the equation y=2x is B. A line that rises from left to right has a slope of 2 and crosses the vertical axis at the point (0, 1).
The correct graph for the equation y=2x is option C.
Explanation:
Option A is not correct because it describes a curve that rises more quickly as x increases, while the equation y=2x describes a straight line.
Option B is also incorrect because it describes a line that rises from left to right and intersects the vertical axis at (0,1), which is not consistent with the equation y=2x.
Option D is not the correct graph because it describes a curve that falls from infinity, passes through the point (-1,2), has a lowest point at (0,1), and then rises again. This does not represent the equation y=2x, which is a straight line.
Therefore, the correct graph for y=2x is option C.
To graph the equation y = 2x on paper, you can follow these steps:
1. Draw a coordinate system with a horizontal x-axis labeled from -5 to 5 and a vertical y-axis labeled from -5 to 5.
2. Choose any x-value (let's say x = 0) and substitute it into the equation to find the corresponding y-value. In this case, when x = 0, y = 2(0) = 0.
3. Plot the point (0, 0) on the coordinate system.
4. Repeat steps 2 and 3 for a few more x-values. For example, when x = 1, y = 2(1) = 2. Plot the point (1, 2) on the graph.
5. Connect the plotted points with a straight line. Since all the points lie on a straight line, this is a linear equation.
Now that you have graphed the equation on paper, you can identify the correct graph from the options provided.
Option B is correct. It shows a line rising from left to right with a slope of 2 and crossing the vertical axis at the point (0, 1), which matches the equation y = 2x.