Answers:
- The equation is y = 2x-3
- The value of m is m = 12
Note: This value of m is not referring to the slope.
The explanation for each question is below.
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Question 2.2.1
Each time x goes up by 1, y goes up by 2
This tells us the slope is rise/run = 2/1 = 2
So we have m = 2 as the slope. This is not to be confused with the m in the table.
The y intercept is b = -3 due to the ordered pair (x,y) = (0,-3). Note that each column is a separate point.
With m = 2 and b = -3, we go from y = mx+b to y = 2x - 3
To check the answer, plug in something like x = 1 to find:
y = 2x-3 = 2(1)-3 = 2-3 = -1
We see that x = 1 leads to y = -1 which is what the table shows. This confirms that (1,-1) is on the line. I'll let you verify the other columns.
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Question 2.2.2
We have the input x = m which is unknown. This is not the slope value.
The table says that the input m leads to the output y = 21
Let's replace y with 21 and solve for m.
y = 2x-3
21 = 2x-3
21+3 = 2x
24 = 2x
24/2 = x
12 = x
x = 12 is the value of m that pairs up with y = 21
In other words, (12, 21) is on the line y = 2x-3
Check:
y = 2x-3
y = 2(12)-3
y = 24-3
y = 21