1. Find the slope, x-intercept and y-intercept of the line joining the points `A(1,3)` and `B(3,5)`

Solution:
The given points are `A(1,3),B(3,5)`

`:. x_1=1,y_1=3,x_2=3,y_2=5`

Using two-points formula, The equation of a line AB is
`(y-y_1)/(y_2-y_1)=(x-x_1)/(x_2-x_1)`

`:. (y-3)/(5-3)=(x-1)/(3-1)`

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

`:. (y-3)/(1)=(x-1)/(1)`

`:. (y-3)=(x-1)`

`:. y -3=x -1`

`:. x-y+2=0`

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

`x-y+2=0`

`:. y=1x+2`

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

`m=1` 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

`:. x-y=-2`

`:. x-(0)=-2`

`:. x=-2`


Hence, the slope of the line is `1`, the x-intercept is `-2` and the y-intercept is `2`

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2. Find the slope, x-intercept and y-intercept of the line joining the points `A(4,-8)` and `B(5,-2)`

Solution:
The given points are `A(4,-8),B(5,-2)`

`:. x_1=4,y_1=-8,x_2=5,y_2=-2`

Using two-points formula, The equation of a line AB is
`(y-y_1)/(y_2-y_1)=(x-x_1)/(x_2-x_1)`

`:. (y+8)/(-2+8)=(x-4)/(5-4)`

`:. (y+8)/(6)=(x-4)/(1)`

`:. (y+8)=6(x-4)`

`:. y +8=6x -24`

`:. 6x-y-32=0`

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

`6x-y-32=0`

`:. y=6x-32`

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

`m=6` and `c=-32`

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

`:. 6x-y=32`

`:. 6x-(0)=32`

`:. 6x=32`

`:. x=16/3`


Hence, the slope of the line is `6`, the x-intercept is `16/3` and the y-intercept is `-32`

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3. Find the slope, x-intercept and y-intercept of the line joining the points `A(7,1)` and `B(8,9)`

Solution:
The given points are `A(7,1),B(8,9)`

`:. x_1=7,y_1=1,x_2=8,y_2=9`

Using two-points formula, The equation of a line AB is
`(y-y_1)/(y_2-y_1)=(x-x_1)/(x_2-x_1)`

`:. (y-1)/(9-1)=(x-7)/(8-7)`

`:. (y-1)/(8)=(x-7)/(1)`

`:. (y-1)=8(x-7)`

`:. y -1=8x -56`

`:. 8x-y-55=0`

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

`8x-y-55=0`

`:. y=8x-55`

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

`m=8` and `c=-55`

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

`:. 8x-y=55`

`:. 8x-(0)=55`

`:. 8x=55`

`:. x=55/8`


Hence, the slope of the line is `8`, the x-intercept is `55/8` and the y-intercept is `-55`

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4. Find the slope, x-intercept and y-intercept of the line joining the points `A(4,8)` and `B(5,5)`

Solution:
The given points are `A(4,8),B(5,5)`

`:. x_1=4,y_1=8,x_2=5,y_2=5`

Using two-points formula, The equation of a line AB is
`(y-y_1)/(y_2-y_1)=(x-x_1)/(x_2-x_1)`

`:. (y-8)/(5-8)=(x-4)/(5-4)`

`:. (y-8)/(-3)=(x-4)/(1)`

`:. (y-8)=-3(x-4)`

`:. y -8=-3x +12`

`:. 3x+y-20=0`

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

`3x+y-20=0`

`:. y=-3x+20`

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

`m=-3` and `c=20`

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+y=20`

`:. 3x+(0)=20`

`:. 3x=20`

`:. x=20/3`


Hence, the slope of the line is `-3`, the x-intercept is `20/3` and the y-intercept is `20`

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