**Example 4**. A manager is considering the cost *C* of printing a book based on the number of pages *p*. He is told that the formula for predicting the cost is linear based on the number of pages and that the *y*-intercept is $4.50 and the slope is $0.027. Find the formula to predict the cost from the number of pages.

**Example 5**. Find the formula for the line with slope 1.35 which has the point (5,40) on it.

We can use this same idea to **compute the formula for a line if we have two points on it** because we can first use the two points to find the slope. Here’s an outline:

Find the formula for of a line through two points.

- Choose the appropriate variable to be the output variable and call it
*y*. Then call the input variable*x*. - Write two points as [latex]({{x}_{1}},{{y}_{1}})[/latex]and [latex]({{x}_{2}},{{y}_{2}})[/latex].
- Use the two points to compute the slope. Call it
*m.* - Pick one of the points (either is fine) and call it [latex]({{x}_{0}},{{y}_{0}})[/latex].
- Plug those values into this equation. [latex](y-{{y}_{0}})=m(x-{{x}_{0}})[/latex]
- Solve for
*y*. That gives the equation of the line. - If different letters are needed besides
*x*and*y*for the input and output variables, replace the*x*and*y*in the formula with those different letters.

**Example 6**: Find the formula for the line through (2,6) and (4,11). Identify the slope and y-intercept.

**Example 7**. We have been told that the amount of oatmeal needed for oatmeal cookies is linearly related to the amount of flour needed. Also, we know that if we use 3 cups of flour, we need 2 cups of oatmeal. And, of course, if we use 0 cups of flour, we will use 0 cups of oatmeal.

- Find the formula to predict the oatmeal needed (called M) from the flour needed (F.)
- Interpret the slope.
- Interpret the y-intercept.

**This last example illustrates that sometimes the intercept is not a number that would be realistic in the situation that the problem describes. But it does have a meaning in the algebraic formula. **

**For a linear formula, the slope is always a number that is meaningful.**