Question

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

Answer 1

`y = - 2` and `x = 2/3`

Explanation:

This is the equation of a straight line. When the line crosses the x-axis the y-coordinate will be zero. By Putting `y = 0` we can find the corresponding value of x (the x-intercept ).

Put `y = 0` : `3x - 2 = 0` so `3x = 2` `rArr x = 2/3`

Similarly , when the line crosses the y-axis the x-coordinate will be zero. Put `x = 0` to find the y-intercept.

Put `x = 0` : `y= 0 - 2` `rArry=-2`

Answer 2

`color(blue)(" y-intercept"->y=-2)`
`color(blue)(" x-intercept"->x=2/3_`

Explanation:

Given:`color(white)(.....) y=3x-2`

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
`color(blue)("To find the x-intercept")`

This is a strait line graph so you will find that the plotted line crosses the y-axis (intercept) at the same value as the constant of `-2`

Why is this?

The y-axis crosses the x-axis at `x=0`. That means that the plot also crosses (intercept) the y-axis at `x=0`. So if we substitute `x=0` into the equation we get:

`y=(3xx0)-2`

`color(blue)("y-intercept"->y=-2)`
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
`color(blue)("To find the x-intercept")`

By the same logic, the plotted line crosses (intercept) the x-axis at y=0. So if we substitute `y=0` into the equation then we have:

`y=3x-2color(white)(.x..) -> color(white)(.x..)color(brown)(0=3x-2)`

Add `color(blue)(2)` to both sides:

`color(brown)(0color(blue)(+2)=3x-2color(blue)(+2))`

`color(green)(2=3x+0)`

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

`color(green)(2/(color(blue)(3))=(3x)/(color(blue)(3))`

`2/3=3/3xx x`

But 3/3 = 1 giving:

`2/3=x`

`color(blue)("x-intercept"->x=2/3_`
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~