Question

Determine the intercepts of the line y+1=3(x-4)

Answer 1

x-intercept =
`(13)/(3)`

y-intercept =
`-13`

Explanation:

We are given the following equation of a line and we are to find the x and y intercepts for it:

`y + 1 = 3 ( x - 4 )`

To find the x-intercept, we will put in 0 for the y to get:

`0 + 1 = 3 ( x - 4 ) \\\\ 1 = 3 x - 12 \\\\ 3 x = 1 + 12 \\\\ x = \frac { 13 } { 3 }`

To find the y-intercept, we will put in 0 for the x to get:

`y + 1 = 3 ( 0 - 4 ) \\\\ y + 1 = -124 \\\\ y = - 12 - 1 \\\\ y = - 13`

So the x-intercept is
`(13)/(3)` while the y-intercept is
`-13`.

Answer 2

To find the intercepts, the other number will be 0 (x-intercept: when y is 0, and vise-versa).

So:

x-intercept: 0 + 1 = 3x - 12 -> 3x = 13 -> x = 13/3, so it will be (
`(13)/(3)`, 0).

y-intercept: y + 1 = 3*0 - 12 -> y = -13, so it will be (0, -13).