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Match the following graph to each equation. All graphs will have a y-intercept of (0,0):y=2/3x+0
A.
Option 1
B.
Option 2
C.
Option 3
Correct Answer B. Option 2
Explanation Option 2 is the correct answer because it represents a linear equation with a y-intercept of (0,0), which matches the given equation y=2/3x+0. The graph in option 2 shows a straight line that passes through the origin (0,0) and has a slope of 2/3, which is consistent with the equation.
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2.
Match the following graph to each equation. All graphs will have a y-intercept of (0,0):y=1x+0
A.
B.
Option 1
C.
Correct Answer A.
Explanation The graph for option 1 matches the equation y=1x+0 because it represents a straight line passing through the origin (0,0) with a slope of 1. This means that for every increase of 1 in the x-coordinate, the y-coordinate also increases by 1. The graph starts at the origin and extends infinitely in both positive x and y directions.
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3.
Match the following graph to each equation. All graphs will have a y-intercept of (0,0):y=-2x+0
A.
B.
C.
Correct Answer B.
Explanation The graph of the equation y = -2x + 0 will be a straight line passing through the origin (0,0) with a slope of -2. As x increases by 1, y will decrease by 2. Therefore, the correct graph will have a downward slope and will pass through the point (0,0).
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4.
Match the following graph to each equation. All graphs will have a y-intercept of (0,0):y=3x+0
A.
B.
C.
Correct Answer A.
Explanation The equation y=3x+0 represents a linear equation in slope-intercept form, where the coefficient of x is 3 and the y-intercept is 0. This means that the graph of this equation will be a straight line passing through the origin (0,0) with a slope of 3. Therefore, the correct graph will be a straight line that starts at the origin and has a steep slope of 3.
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5.
Match the following graph to each equation. All graphs will have a y-intercept of (0,0):y=-5x+0
A.
B.
C.
Correct Answer A.
Explanation The equation y=-5x+0 represents a linear function with a negative slope of -5. Since the y-intercept is (0,0), this means that the graph will pass through the origin. As x increases, y will decrease by 5 times the value of x. Therefore, the graph will start at the origin and slope downwards to the right.