Question

Find x- and y-intercepts. Write ordered pairs representing the points where the line crosses the axes.

1. y=5x−10
2. y=2x−3
3. x+4y=12
4. x−y=4
5. y=−2x
6. y−4x=0
7. 0.3x−0.4y=0.7
8. y= 2/3 x− 1/3

Answer 1

1.
`y=5x-10`

To find the x-intercept of the given linear equation , plug in y=0 and solve for x.

`y=5x-10`

`0=5x-10`

`10=5x`

∴
`x=2`

Now, to find the y-intercept for the given linear equation we plug in x=0 and solve for y.

`y=5x-10`

`y=5(0)-10`

`y=0-10`=
`-10`

∴ y=-10.

The ordered pairs representing the points where the line
`y=5x-10` crosses the axes are,
`(2,0)` and
`(0, -10)`.

2.
`y=2x-3`

To find the x-intercept of the given linear equation , plug in y=0 and solve for x.

`y=2x-3`

`0=2x-3`

`3=2x`

∴
`x=(3)/(2)`

Now, to find the y-intercept for the given linear equation we plug in x=0 and solve for y.

`y=2x-3`

`y=2(0)-3`

`y=0-3`=
`-10`

∴ y=-3.

The ordered pairs representing the points where the line
`y=2x-3` crosses the axes are,
`((3)/(2) ,0)` and
`(0, -3)`.

3.
`x+4y=12`

To find the x-intercept of the given linear equation , plug in y=0 and solve for x.

`x+4y=12`

`x+4\cdot (0)=12`

`x+0=12`

∴
`x=12`

Now, to find the y-intercept for the given linear equation we plug in x=0 and solve for y.

`x+4y=12`

`0+4y=12`

`4y=12`

∴ y=3.

The ordered pairs representing the points where the line
`x+4y=12` crosses the axes are,
`(12, 0)` and
`(0, 3)`.

4.
`x-y=4`

To find the x-intercept of the given linear equation , plug in y=0 and solve for x.

`x-y=4`

`x-0=4`

∴
`x=4`

Now, to find the y-intercept for the given linear equation we plug in x=0 and solve for y.

`x-y=4`

`0-y=4`

`y=-4`

∴ y=-4.

The ordered pairs representing the points where the line
`x-y=4` crosses the axes are,
`(4, 0)` and
`(0, -4)`.

5.
`y=-2x`

To find the x-intercept of the given linear equation , plug in y=0 and solve for x.

`y=-2x`

`0=-2x`

∴
`x=0`

Now, to find the y-intercept for the given linear equation we plug in x=0 and solve for y.

`y=-2\cdot(0)`

`y=0`

`y=0`

∴ y=0.

The ordered pairs representing the points where the line
`y=-2x` crosses the axes is,
`(0, 0)`

6.
`y-4x=0`

To find the x-intercept of the given linear equation , plug in y=0 and solve for x.

`y-4x=0`

`0-4x=0`

`-4x=0`

∴
`x=0`

Now, to find the y-intercept for the given linear equation we plug in x=0 and solve for y.

`y-4x=0`

`y-4\cdot (0)=0`

`y-0=0`

∴ y=0.

The ordered pairs representing the points where the line
`y-4x=0` crosses the axes is,
`(0,0)`

7.
`0.3x-0.4y=0.7`

To find the x-intercept of the given linear equation , plug in y=0 and solve for x.

`0.3x-0.4\cdot (0)=0.7`

`0.3x-0=0.7`

`x=(0.7)/(0.3)`

∴
`x=(7)/(3)`

Now, to find the y-intercept for the given linear equation we plug in x=0 and solve for y.

`0.3\cdot(0)-0.4y=0.7`

`0-0.4y=0.7`

`-0.4y=0.7`

`y=-(0.7)/(0.4)`

∴
`y=-(7)/(4)`

The ordered pairs representing the points where the line
`0.3x-0.4y=0.7` crosses the axes are,
`((7)/(3) , 0)` and
`(0, -(7)/(4) )`.

8.
`y=(2)/(3)x-(1)/(3)`

To find the x-intercept of the given linear equation , plug in y=0 and solve for x.

`0=(2)/(3)x-(1)/(3)`

`(2)/(3)x=(1)/(3)`

`x=(1)/(3)\cdot (3)/(2)`

∴
`x=(1)/(2)`

Now, to find the y-intercept for the given linear equation we plug in x=0 and solve for y.

`y=(2)/(3)\cdot (0)-(1)/(3)`

`y=0-(1)/(3)`

∴
`y=-(1)/(3)`

The ordered pairs representing the points where the line
`y=(2)/(3)x-(1)/(3)` crosses the axes are,
`((1)/(2), 0)` and
`(0, -(1)/(3) )`