Slope as Unit Rate Quick Check
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Question
Use the image to answer the question.
An illustration shows a coordinate plane with the x-axis ranging from negative 9 to 9 in one unit increments, and the y-axis ranging from negative 11 to 11 in one unit increments. A solid line passes through two plotted points and extends beyond. A solid line with arrows at both ends passes through points with coordinates left parenthesis 0 comma 0 right parenthesis and left parenthesis 6 comma 6 right parenthesis.
Explain why the slope is positive or negative.
(1 point)
Responses
The slope is positive because the line decreases as you move from left to right on the graph.
The slope is positive because the line decreases as you move from left to right on the graph.
The slope is negative because the line increases as you move from left to right on the graph.
The slope is negative because the line increases as you move from left to right on the graph.
The slope is negative because the line decreases as you move from left to right on the graph.
The slope is negative because the line decreases as you move from left to right on the graph.
The slope is positive because the line increases as you move from left to right on the graph.
The correct answer is: The slope is positive because the line increases as you move from left to right on the graph.
The correct answer is: The slope is positive because the line increases as you move from left to right on the graph.
To determine whether the slope is positive or negative, you need to analyze the direction of the line on the graph. Here's how you can do it:
1. Locate the two plotted points mentioned in the question: (0, 0) and (6, 6).
2. Observe the position of these points on the coordinate plane.
- (0, 0) is the point where the line intersects the y-axis.
- (6, 6) is a point on the line that is six units to the right and six units up from the origin (0, 0).
3. Compare the y-values of the two points.
- The y-value at (6, 6) is the same as the y-value at (0, 0), indicating that the line is neither increasing nor decreasing.
4. Consider the x-values of the two points.
- The x-value at (6, 6) is greater than the x-value at (0, 0), suggesting that the line is moving from left to right.
5. Based on the line moving from left to right and the y-values remaining constant, determine the slope.
- If the line moves up as you move from left to right, the slope is positive.
- If the line moves down as you move from left to right, the slope is negative.
Using this analysis, it can be concluded that the slope is positive because the line remains constant (neither increasing nor decreasing) as you move from left to right on the graph. Therefore, the correct answer is: "The slope is positive because the line increases as you move from left to right on the graph."