1. Find the slope, x-intercept and y-intercept of the line `2x+3y=4`

Solution:
The given equation sholud be written in the form `y=mx+c`

`2x+3y=4`

`:. 3y=-2x+4`

`:. y=-2/3x+4/3`

Comparing this equation with `y=mx+c`, we get

`m=-2/3` and `c=4/3`

Now, to find the intercept on X-axis put `y=0` in the given equation.

The value of `x` will give the intercept of the line on X-axis

`:. 2x+3y=4`

`:. 2x+3(0)=4`

`:. 2x=4`

`:. x=2`


Hence, the slope of the line is `-2/3`, the x-intercept is `2` and the y-intercept is `4/3`

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2. Find the slope, x-intercept and y-intercept of the line `2x+3y-6=0`

Solution:
The given equation sholud be written in the form `y=mx+c`

`2x+3y-6=0`

`:. 3y=-2x+6`

`:. y=-2/3x+2`

Comparing this equation with `y=mx+c`, we get

`m=-2/3` and `c=2`

Now, to find the intercept on X-axis put `y=0` in the given equation.

The value of `x` will give the intercept of the line on X-axis

`:. 2x+3y=6`

`:. 2x+3(0)=6`

`:. 2x=6`

`:. x=3`


Hence, the slope of the line is `-2/3`, the x-intercept is `3` and the y-intercept is `2`

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3. Find the slope, x-intercept and y-intercept of the line `3x+6y-8=0`

Solution:
The given equation sholud be written in the form `y=mx+c`

`3x+6y-8=0`

`:. 6y=-3x+8`

`:. y=-1/2x+4/3`

Comparing this equation with `y=mx+c`, we get

`m=-1/2` and `c=4/3`

Now, to find the intercept on X-axis put `y=0` in the given equation.

The value of `x` will give the intercept of the line on X-axis

`:. 3x+6y=8`

`:. 3x+6(0)=8`

`:. 3x=8`

`:. x=8/3`


Hence, the slope of the line is `-1/2`, the x-intercept is `8/3` and the y-intercept is `4/3`

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4. Find the slope, x-intercept and y-intercept of the line `4x+5y+7=0`

Solution:
The given equation sholud be written in the form `y=mx+c`

`4x+5y+7=0`

`:. 5y=-4x-7`

`:. y=-4/5x-7/5`

Comparing this equation with `y=mx+c`, we get

`m=-4/5` and `c=-7/5`

Now, to find the intercept on X-axis put `y=0` in the given equation.

The value of `x` will give the intercept of the line on X-axis

`:. 4x+5y=-7`

`:. 4x+5(0)=-7`

`:. 4x=-7`

`:. x=-7/4`


Hence, the slope of the line is `-4/5`, the x-intercept is `-7/4` and the y-intercept is `-7/5`

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