Question

How do you find the x and y intercepts of `y=3x-2`?

Answer 1

`"x-intercept "=2/3," y-intercept "=-2`

Explanation:

`"To find the intercepts, that is where the graph crosses"`
`"the x and y axes"`

`• " let x = 0, in the equation for y-intercept"`

`• " let y = 0, in the equation for x-intercept"`

`x=0rArry=0-2=-2larrcolor(red)"y-intercept"`

`y=0rArr3x-2=0rArrx=2/3larrcolor(red)"x-intercept"`
graph{(y-3x+2)((x-0)^2+(y+2)^2-0.04)((x-2/3)^2+(y-0)^2-0.04)=0 [-10, 10, -5, 5]}

Answer 2

`"y-intercept " = (0, -2) or -2`
`"y-intercept " = (2/3, 0) or 2/3`

Explanation:

The y-intercept is when the value of `x = 0`. Therefore, plugging in the value of `x` into the equation:

`3(0) - 2 = -2 " So, " y = -2` This is for the y-intercept

The x intercept is when `y = 0`, substituting this into the equation gives us:

`0 = 3x - 2` It is possible to rearrange this:

`0 -3x = 3x - 3x - 2`
`3x = 2`
`x = 2/3`