The line below has slope 3. Find the indicated number.
The slope is 3 and Δ x = 2, so
Δ y = slope × Δ x = 3(2) = 6.
To find the missing value of y, we add yold = -1 and Δ y = 6 to get ynew = 5.
The line below has slope . Find the indicated number.
The slope is and Δ x = 3.
Then we add yold = 5 and to get
The line below has slope 0.2. Find the indicated number.
The missing value is Δ y (we aren't told yold, so we couldn't find ynew anyway).
The slope is 0.2 and Δ x = 3, so
Δ y = (0.2)(3) = 0.6.
Find the indicated number.
This problem has one more step than the others, because first we need to figure out the slope of the line.From the first two points we can calculate
Now let's ignore the point (1,2). Look only at these two points, and think yold = 5 and Δ x = 3.
Again, we need to find the slope of this line. Looking at the outermost two points we can calculate rise and run.
The picture in this case is a little misleading. Since the point whose y-value we want to know is to the left of the point whose y-value we know, Δ x is negative.
Since both the slope and Δ x are negative, their product Δ y is positive:
ynew = yold + Δ y = 7 + 10 = 17.
This makes sense: given the picture, we would expect ynew to be larger than yold.
We have yold = 3 and Δ x = -3.
From the picture, we expect ynew to be less than yold.
The line below has slope -7. Find the indicated number.
In this problem we are asked to find Δ y. Look carefully at the picture, and make sure to use -2, not + 2, for Δ x.
Δ y = slope × Δ x = (-7)(-2) = 14.
Make it rain.