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

$y-y_1=m(x-x_1)$

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


$y-y_1=m(x-x_1)$


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

$m = \frac{1}{4}$


We apply the point-slope formula


$y-y_1=m(x-x_1)$


to obtain,



$y + 8 = \frac{1}{4} (x - 4)$


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.