Chapter 8.3, Problem 31E

To determine

To find:

The three values of c for which both the x -intercept and the y -intercept are integers. How are your values of c related to the coefficients of x and y in the given equation?

Answer to Problem 31E

The required three values of c would be $-12,12,24$ .

The values of c will decide the x - and y -intercept of our given equation.

Explanation of Solution

Given:

An equation: $4x+6y=c$

Calculation:

Upon looking at our given equation, we can see that it is in standard form of equation $Ax+By=C$ , where A , B and C are integers.

We know that to find x -intercept, we substitute $y=0$ in given equation and solve for x . Similarly, to find y -intercept, we substitute $x=0$ in given equation and solve for y .

The value of c will be numbers, which are multiples of both 4 and 6 or divisible by both 4 and 6.

We know that least common multiple of 4 and 6 is 12. $-12\text{and }24$ are other two multiples of both 4 and 6.

Therefore, our required three values of c would be $-12,12,24$ .

The values of c will decide the x - and y -intercept of our given equation.