Differential Equations Exercises

Answer

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 y_old = -1 and Δ y = 6 to get y_new = 5.

Answer

The slope is and Δ x = 3.

This means

Then we add y_old = 5 and to get

Answer

The missing value is Δ y (we aren't told y_old, so we couldn't find y_new anyway).

The slope is 0.2 and Δ x = 3, so

Δ y = (0.2)(3) = 0.6.

Answer

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 y_old = 5 and Δ x = 3.

Then

and

Answer

Again, we need to find the slope of this line. Looking at the outermost two points we can calculate rise and run.

So

We get

and

Answer

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:

so

y_new = y_old + Δ y = 7 + 10 = 17.

This makes sense: given the picture, we would expect y_new to be larger than y_old.

Answer

We have y_old = 3 and Δ x = -3.

From the picture, we expect y_new to be less than y_old.

Answer

In this problem we're asked to find Δ y. Look carefully at the picture, and make sure to use -2, not + 2, for Δ x.

We get

Δ y = slope × Δ x = (-7)(-2) = 14.