Question

How do you find the x and y intercept of `y = 3x – 8`?

Answer 1

Solution provided in extreme detail.

`x_("intercept")=8/3`

`y_("intercept")= -8`

Explanation:

`color(blue)("Determin the y intercept")`

Consider the standardised format of `y=mx+c`

`color(blue)(y_("intercept")=c = -8)`
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
`color(blue)("Determine the x intercept")`

The x-intercept is when y = 0 because that is the value of y where the x-axis crosses it

Set y = 0 giving:`" "0=3x-8`

Add `color(red)(8)` to both sides

`color(green)(0color(red)(+8)" "=" "3x-8color(red)(+8))`

But `-8+8=0` giving:

`8=3x`

Divide both sides by `color(red)(3)`

`color(green)(8/(color(red)(3))=3/(color(red)(3))x)`

But `3/3=1 and 1xx x = x` giving:

`8/3=x`

Write as `color(blue)(x_("intercept")=8/3)`