Question

How do you find the x and y intercepts of `3x-4y-10=0`?

Answer 1

The intercepts are at `(3 1/3, 0) and (0,-2 1/2)`

Explanation:

Finding the intercepts is a very easy and very useful skill to develop for drawing graphs. It is particularly handy for linear programming.

All along the `x`-axis, `y=0` All points are `(x, 0)`

All along the `y`-axis, `x=0` All points are `(y, 0)`

To find the `x`-intercept, set `y=0` and solve for `x`

To find the `y`-intercept, set `x=0` and solve for `y`

The only time this does not work is if the graph goes through the origin.

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

`3x-4y-10 =0" "rarr 3x -4y =10`

For the `x`-int: `y=0`
`" "3x -4(0) = 10" "rarr3x=10" "x= 3 1/3`

For the `y`-int: `x=0`
`" "3(0) -4y = 10" "rarr-4y=10" "y= -5/2`

The intercepts are at `(3 1/3, 0) and (0,-2 1/2)`

Answer 2

The x-intercept is `(10/3, 0)=(3 1/3,0)`.

The y-intercept is `(0,-5/2)=(0, -2 1/2)`

See the explanation for the process.

Explanation:

Find x and y intercepts. The x-intercept is the point where `y` is `0`. The y-intercept is the point where `x` is `0`.

Given

`3x-4y-10=0`

X-intercept

Substitute `0` for `y`.

`3x-4(0)-10=0`

Simplify.

`3x-10=0`

Add `10` to both sides.

`3xcolor(red)cancel(color(black)(-10))+color(red)cancel(color(black)(10))=0+10`

Simplify.

`3x=10`

Divide both sides by `3`.

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

`x=10/3`

The x-intercept is `(10/3, 0)=(3 1/3,0)`.

Y-intercept

Substitute `0` for the `x`. Solve for `y`.

`3(0)-4y-10=0`

Simplify.

`-4y-10=0`

Add `10` to both sides.

`-4y=10`

Divide both sides by `-4`.

`y=10/(-4)`

`y=-10/4`

Simplify.

`y=-5/2`

The y-intercept is `(0,-5/2)=(0, -2 1/2)`

Use the graph below to check the x and y intercepts.

graph{3x-4y-10=0 [-16.02, 16, -8.01, 8.01]}