SOLUTION: write an equation in standard form of a line whose x-intercept is an integer and y-intercept is a fraction. Explain how you know that the x-intercept is an integer and y-intercept

Question 999176: write an equation in standard form of a line whose x-intercept is an integer and y-intercept is a fraction. Explain how you know that the x-intercept is an integer and y-intercept is a fraction
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
ax + by = c

the x-intercept is the value of x when y = 0.
the y-intercept is the value of y when x = 0.

when y = 0, ax = c which results in x = c/a

when x = 0, by = c which results in y = c/b

in order for c/a to be an integer, c has to be a multiple of a.

in order for c/b to be a fraction, c must not be a multiple of b.

if c is a multiple of a, then c can be made equal to a*d, where d is an integer.

example:

55 / 5 is an integer because 55 is a multiple of 5.
55 = 5 * 11, so 55/5 = 11

56 / 5 is not an integer because 56 is not a multiple of 5.

-15 / 5 is an integer because 15 is a multiple of 5.
15 = 5 * 3, so 15/5 = 3

-16 / 5 is not an integer because 16 is not a multiple of 5.

so, if you want ax + by = c to have the x-intercept an integer and the y-intercept a fraction, then c must be a multiple of a but not a multiple of b.

an example would be:

5x + 6y = 15

the x intercept is the value of x when y = 0.
when y = 0, the equation becomes 5x = 15.
solve for x to get x = 15/5 = 3.
3 is an integer.

the y intercept is the value of y when x = 0.
when x = 0, the equation becomes 6y = 15.
solve for y to get y = 15/6.
15/6 is not an integer.

that's my take.

an integer can also be described as a fraction where the denominator is equal to 1.

why is 55/5 an integer?

multiply numerator and denominator of 55/5 by 1/5 and you get (55*1/3) / (5*1/5) which results in 11/1 which is the same as 11.

55/5 is therefore an integer because it can be simplified to a ratio where the denominator is equal to 1.

56/5 cannot be simplified to a ratio where the numerator is an integer and the denominator is equal to 1.

this is because 56 is not a multiple of 5.

you can find a number such that the denominator is 1, but the number will not be an integer.

56/5 = 11.2/1 = 11.2 which is a fraction in decimal form.

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