Question

Please answer and explain these 3 questions. Thank you!

Answer 1

QUESTION 1

We want to find the equation of the straight line that passes through the point

`(1,24)`
and has slope

`m = - 0.6`


We use the point slope formula


`image`

to obtain,


`y - 24 = - 0.6(x - 1)`


We multiply through by 10 to get,



`10y - 240 = - 6(x - 1)`


We expand bracket to get,


`10y - 240 = - 6x + 6`


We group the constants on the right hand side to get,



`10y + 6x = 6 + 240`


we simplify to get,


`10y + 6x = 246`

Divide through by 2,



`5y + 3x = 123`

or


`3x + 5y = 123`

The correct answer is H.



QUESTION 2


We want to find the equation of a line that passes through

`(6,-8)`
with slope

`m = 0`

We apply the point slope formula



`image`


to obtain,



`y + 8 = 0(x - 6)`



`y + 8 = 0`



`y = - 8`

The correct answer is J.


QUESTION 3


We want to find the equation of the straight line that passes through,


`(4,-8)`

and has slope


`m = (1)/(4)`


We apply the point-slope formula



`image`


to obtain,




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


Let us multiply through by 4 to get,



`4y + 32 = x - 4`
We group the constant terms on the right hand side to obtain,


`4y - x = - 4 - 32`

This simplifies to,


`4y - x = - 36`

We multiply through by -1 to get,



`x - 4y = 36`

The correct answer is A.