Question

Find an equation of the line in the form ax + by = c whose x-intercept is 10 and y-intercept is 5, where a, b, and c are integers with no factor common to all three, and a ≥ 0.

Answer 1

To find the equation of the line in the form ax + by = c with x-intercept 10 and y-intercept 5, we can determine the values of a, b, and c. By representing the x-intercept as 10a and the y-intercept as 5b, and finding an equation that satisfies these conditions, we can obtain the equation 5x + 10y = 100.

Step-by-step explanation:

To find the equation of a line in the form ax + by = c, with x-intercept of 10 and y-intercept of 5, we need to determine the values of a, b, and c.

1. To find c, we can use the x-intercept. When x = 10, the equation becomes 10a + 0b = c. Since the x-intercept is 10, c = 10a.
2. To find b, we can use the y-intercept. When y = 5, the equation becomes 0a + 5b = c. Since the y-intercept is 5, c = 5b.
3. Substituting the value of c from step 1 into step 2, we get 10a = 5b.

Therefore, we can choose any values for a and b that satisfy the equation 10a = 5b. For example, if we let a = 5 and b = 10, the equation becomes 50 + 50 = c. So, c = 100.

As a result, an equation that satisfies the given conditions is 5x + 10y = 100.