Answer: Choice A
Answer for the box: (-7/2)x+3
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Step-by-step explanation:
The table shows that x = 0 leads to y = f(x) = 3. This immediately tells us the y intercept is b = 3. The y intercept occurs whenever x = 0.
To find the slope, note how each time x goes up by 2, y decreases by 7. So we can say
slope = rise/run
slope = (change in y)/(change in x)
slope = -7/2
We can write that as -3.5
If you want to apply the slope formula, then you can do so on any two points from the table. I'll pick on the first two columns
m = (y2-y1)/(x2-x1)
m = (3-10)/(0-(-2))
m = (3-10)/(0+2)
m = -7/2
m = -3.5
So we can say that y = mx+b turns into y = (-7/2)x+3 since we found m = -7/2 and b = 3
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As a check, plugging x = -2 into the equation leads to...
y = (-7/2)x+3
y = (-3.5)*(-2)+3
y = 7+3
y = 10
This verifies the first column of the table. I'll let you check the other columns.