Question

The equation `3x+1.5y = 30` describes the number of burgers and hot dogs a family can buy with $30. What are the intercepts of the equation, and what does each represent?

Answer 1

Basically the intercepts represent the number of one of the items you can buy using the entire amount of `$30`.

Explanation:

Have a look:

Answer 2

See a solution process below:

Explanation:

`x`-intercept: To find the `x` intercept set `y` to `0` and solve for `x`:

`3x + (1.5 xx 0) = 30`

`3x + 0 = 30`

`3x = 30`

`(3x)/color(red)(3) = 30/color(red)(3)`

`(color(red)(cancel(color(black)(3)))x)/cancel(color(red)(3)) = 10`

`x = 10` or `(10, 0)`

`y`-intercept: To find the `y` intercept set `x` to `0` and solve for `x`:

`(3 xx 0) + 1.5y = 30`

`0 + 1.5y = 30`

`1.5y = 30`

`(1.5y)/color(red)(1.5) = 30/color(red)(1.5)`

`(color(red)(cancel(color(black)(1.5)))y)/cancel(color(red)(1.5)) = 20`

`y = 20` or `(0, 20)`

The intercepts represent the maximum number of hotdogs or hamburgers the family could by,

So for example, if they bought no hotdogs (the y value equal to 0) they could buy 10 hamburgers, the `x`-intercept.

Answer 3

x intercept represents `10` burgers only can be bought in `$30` , y intercept represents `20` hot dogs only can be bought in `$30`

Explanation:

`3 x+ 1.5 y=30`

Let `x` be the number of burgers of `$3` cost per unit

and `y` be the number of hot dogs of `$1.5` cost per unit

x intercept is found by putting `y=0` in the equation.

`3 x +1.5*0=30 or 3 x = 30 or x= 10` , It reveals that

`10` burgers alone can be bought in `$30`

y intercept is found by putting `x=0` in the equation.

`3*0 +1.5 y=30 or 1.5 y = 30 or y= 30/1.5=20` , It reveals

that `20` hot dogs alone can be bought in `$30`

x intercept represent `10` burgers only can be bought in `$30`

y intercept represent `20` hot dogs only can be bought in `$30`

graph{3 x+1.5 y=30 [-80, 80, -40, 40]} [Ans]

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