Match each equation with the graph that it most closely resembles. (Hint: Determining the signs of m and b will help you make your decision.)
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Part 1
y=−x
y=3
y=−x−3
y=−3
y=−x+3
y=x
y=x−3
y=x+3
Drag each equation above to the correct graph below.
Graph A
x
y
A graph labeled A has a coordinate system with an unlabeled horizontal x-axis and an unlabeled vertical y-axis. A line rises from left to right, intersects the x-axis at a point to the left of the origin and intersects the y-axis at a point above the origin.
Graph E
x
y
A graph labeled E has a coordinate system with an unlabeled horizontal x-axis and an unlabeled vertical y-axis. A horizontal line intersects the y-axis at a point below the origin.
Graph B
x
y
A graph labeled B has a coordinate system with an unlabeled horizontal x-axis and an unlabeled vertical y-axis. A horizontal line intersects the y-axis at a point above the origin.
Graph F
x
y
A graph labeled F has a coordinate system with an unlabeled horizontal x-axis and an unlabeled vertical y-axis. A line rises from left to right, intersects the y-axis at a point below the origin and intersects the x-axis at a point to the right of the origin.
Graph C
x
y
A graph labeled C has a coordinate system with an unlabeled horizontal x-axis and an unlabeled vertical y-axis. A line falls from left to right, intersects the x-axis at a point to the left of the origin and intersects the y-axis at a point below the origin.
Graph G
x
y
A graph labeled G has a coordinate system with an unlabeled horizontal x-axis and an unlabeled vertical y-axis. A line falls from left to right, passing through the origin.
Graph D
x
y
A graph labeled D has a coordinate system with an unlabeled horizontal x-axis and an unlabeled vertical y-axis. A line falls from left to right, intersects the y-axis at a point above the origin and intersects the x-axis at a point to the right of the origin.
Graph H
x
y
A graph labeled H has a coordinate system with an unlabeled horizontal x-axis and an unlabeled vertical y-axis. A line rises from left to right, passing through the origin.
y=−x - Graph H
y=3 - Graph B
y=−x−3 - Graph F
y=−3 - Graph E
y=−x+3 - Graph G
y=x - Graph D
y=x−3 - Graph C
y=x+3 - Graph A
To match each equation with the graph, we need to analyze the equations and compare them with the characteristics of each graph.
1. The equation y = -x represents a line that starts from the origin and falls as you move from left to right. This matches with Graph D.
2. The equation y = 3 represents a horizontal line that intersects the y-axis at a point above the origin. This matches with Graph B.
3. The equation y = -x - 3 represents a line that starts from the origin and falls as you move from left to right. Additionally, it intersects the y-axis at a point below the origin. This matches with Graph C.
4. The equation y = -3 represents a horizontal line that intersects the y-axis at a point below the origin. This matches with Graph E.
5. The equation y = -x + 3 represents a line that starts from the origin and falls as you move from left to right. Additionally, it intersects the y-axis at a point above the origin. This matches with Graph F.
6. The equation y = x represents a line that starts from the origin and rises as you move from left to right. This matches with Graph H.
7. The equation y = x - 3 represents a line that starts from the origin and rises as you move from left to right. Additionally, it intersects the y-axis at a point below the origin. This matches with Graph G.
8. The equation y = x + 3 represents a line that starts from the origin and rises as you move from left to right. Additionally, it intersects the y-axis at a point above the origin. This matches with Graph A.
So, the correct matching is:
1. Graph D
2. Graph B
3. Graph C
4. Graph E
5. Graph F
6. Graph H
7. Graph G
8. Graph A
To match each equation with the graph that it most closely resembles, we need to consider the characteristics of each equation.
1. The equation y = −x represents a line with a negative slope that passes through the origin. This graph can be matched to Graph H because it also has a line rising from left to right and passing through the origin.
2. The equation y = 3 represents a horizontal line parallel to the x-axis, intersecting the y-axis at y = 3. This graph matches Graph B because it also has a horizontal line intersecting the y-axis above the origin.
3. The equation y = −x − 3 represents a line with a negative slope that intersects the y-axis below the origin. This matches Graph F because it has a line rising from left to right, intersecting the y-axis below the origin.
4. The equation y = −3 represents a horizontal line parallel to the x-axis, intersecting the y-axis at y = −3. This matches Graph C because it also has a horizontal line intersecting the y-axis below the origin.
5. The equation y = −x + 3 represents a line with a negative slope that intersects the y-axis above the origin. This matches Graph D because it has a line falling from left to right, intersecting the y-axis above the origin.
6. The equation y = x represents a line with a positive slope that passes through the origin. This matches Graph G because it also has a line falling from left to right and passing through the origin.
7. The equation y = x − 3 represents a line with a positive slope that intersects the y-axis below the origin. This matches Graph A because it has a line rising from left to right, intersecting the x-axis to the left of the origin and the y-axis above the origin.
8. The equation y = x + 3 represents a line with a positive slope that intersects the y-axis above the origin. This matches Graph E because it has a line falling from left to right, intersecting the x-axis to the right of the origin and the y-axis below the origin.
By considering the signs of the slope (m) and y-intercept (b) of each equation, we can determine which graph resembles each equation the most.