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The number we want is the sum of Δ y and the value of y at the first point. therefore the missing number is
4 + 1 = 5.
When doing problems like this, it can be helpful to think about the values as yold and ynew.
yold is usually the value of y we're given in the problem. If we add yold and the change in y, we get ynew.
ynew = yold + Δ y.
The line below has a slope of -0.7. Find the indicated number.
We have yold = 3 and we want to find ynew. We know
ynew = yold + Δ y,
so we just need to find Δ y, which we know how to do:
Δ y = slope × Δ x = (-0.7)(4.5) = -3.15.
Now we know
ynew = 3 + (-3.15) = -0.15.
The function f is a line with slope . If f (a) = 3, what is ?
The function f is a line with slope that passes through the point (a, 3). The old value of f is 3 and we want to know the new value of f if we change x by :
We don't know what a is, but that's ok. We know , so
To get the new value of f, we add Δ y to the old value of f:
The line below has a slope of 2. Find the indicated number.
We use the same formula as before. The slope is 2 and Δ x = -0.5, so
Δ y = 2(-0.5) = -1.
ynew = yold + (-1) = 4 - 1 = 3.
This makes sense, if you think about it. Having a slope of 2 means for every step of size 1 that x moves right, y should move up 2. This means if x moves to the right by 0.5, y should move up by 1. So the value of y when x = 4 should be one more than the value of y when x = 3, which is what happens.