Question

Find the coordinates of the points A and B where the line 5x+y=10 cuts x-axis and y-axis respectively?

Answer 1

The x-intercept is Point A: `(2,0)`.

The y-intercept is Point B: `(0,10)`

Explanation:

The line cuts the x-axis and y-axis at the x-intercept and the y-intercept.

X-intercept: value of `x` when `y=0`

Substitute `0` for `y`, and solve for `x`.

`5x+0=10`

`5x=10`

Divide both sides by `5`.

`x=10/5`

`x=2`

Point A: `(2,0)` `larr` x-intercept

Y-intercept: value of `y` when `x=0`

Substitute `0` for `x`.

`5(0)+y=10`

Simplify.

`0+y=10`

`y=10`

Point B: `(0,10)` `larr` y-intercept

graph{5x+y=10 [-14.24, 14.23, -7.12, 7.12]}

Answer 2

x-axis `A=(2,0)`
y-axis `B=(0,10)`;

Explanation:

`5x+y=10` is the equation of a straight line.
When you want to find the intersection of a straight line with the axis you basically want to know what is the value of `y` when `x` is equal to `0` (y-axis intercection) and what is the value of `x` when `y` is equal to `0` (x-axis intecection).
x-axis:
when `y=0` the equation becomes:
`5x+0=10=>x=10/5=>x=2`
so the first point is `A=(2,0)`

y-axis:
when `x=0` the equation becomes:
`0+y=10=>y=10`
so the second point is `B=(0,10)`
graph{5x+y=10 [-10, 10, -5, 5]}

Answer 3

`A(2,0)" and "B(0,10)`

Explanation:

`"to find where the line 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=0rArr0+y=10rArry=10larrcolor(red)"y-intercept"`

`y=0rArr5x+0=10rArrx=2larrcolor(red)"x-intercept"`

`"crosses x-axis at "A(2,0)" and y-axis at "B(0,10)`
graph{(y+5x-10)((x-2)^2+(y-0)^2-0.04)((x-0)^2+(y-10)^2-0.04)=0 [-20, 20, -10, 10]}