Question

which equation represents the line that passes through the points (6 –3) and (–4 –9)

Answer 1

OK - straight lines have an equation of general form

y=mx+b

where m is the gradient, and b is the y value when x=0 (known as the y intercept)

Given 2 points you can work out the gradient

in your case

x1 = 6
y1 = -3

x2= -4
y2= -9

gradient is given by

\[gradient = \frac{ y _{2}-y _{1} }{x _{2}-x _{1} }\]

Answer 2

so now you have the value for the gradient m

so the general formula is y = mx+b (and oyu know m) so the only unknown is b

but oyu know 2 of the points which lie on the line - so pick one of them - lets say (6,-3)

so y=-3, x=6

-3 = m(6) +b

since you know m you can solve the above equation for b

and then the answer is
y=mx+b where you put in the values you calculated for m and b

Answer 3

the answer choices are:
y+4=3/5(x+9)
y+4=5/3(x+9)
y-3=3/5(x+6)
y+3=3/5(x-6)

Answer 4

I don't really care what the answer choices are.

The information above is ALL you need to work out the answer for yourself.

SO posting the answer choices AFTER I have given you all that information is a kind of indication that you don't really want to know HOW to do it after all!