What is the next number in the pattern below?
2 answers:
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See the attached image to see how all of the answers fill out.
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Problem 6a
The slope of line A is -1/1 or just -1
The reason why is because we start at (0,3) and move down 1 and over to the right 1 to get to the next point (1,2). Alternatively you can use the slope formula m = (y2-y1)/(x2-x1) to get the same result.
Since the slope of line A is -1, this means that we'll write "-1" in the first row of the "constant rate of change" column.
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The two points (0,2) and (1,3) are on the line B
Use the slope formula to get
m = (y2-y1)/(x2-x1)
m = (3-2)/(1-0)
m = 1/1
m = 1
The slope of line B is 1. Write "1" in the second row of the "constant rate of change" column.
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The points (0,-4) and (1,-2) are on line C
Slope:
m = (y2-y1)/(x2-x1)
m = (-2-(-4))/(1-0)
m = (-2+4)/(1-0)
m = 2/1
m = 2
The slope of line C is 2, which is written in the last row of the "constant rate of change" column.
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Now onto the y intercept column.
Line A crosses the y intercept at the point (0,3) or simply 3 on the y axis. So we'll have 3 in the first row.
Write 2 in the next row under the "3" to indicate that the y intercept of line B is 2. The black line B crosses the y axis at 2 on the vertical number line.
Similarly, the y intercept for line C is -4. This red line crosses the vertical y axis at -4
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Now onto the x intercept
The x intercept of line A is 3. This is where the blue line crosses the horizontal x axis.
The x intercept of line B is -2. This is where the black line crosses the horizontal x axis.
The x intercept of line C is 2. This is where the red line crosses the horizontal x axis.
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Problem 6b
Equation D: y = 2+x
is the same as
y = x+2
The slope here is 1 (since y = x+2 is the same as y = 1x+2) and the y intercept is 2.
The fact that
Slope = 1
and
y intercept = 2
means we have a match with line B
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The equation y = -4+2x is the same as y = 2x-4
Slope = 2
y intercept = -4
this matches with line C
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y = 3-x is the same as y = -x+3
which can be written as y = -1x+3
Slope = -1
y intercept = 3
This matches with line A
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See the attached image to see how all of the answers fill out.
