Question

What is the equation of the line, in standard form, that passes through (4, -3) and is parallel to the line whose equation is 4x + y - 2 = 0?

Answer 1

alright so i would recommend first putting your given equation into slope-intercept form

Answer 2

to do that you just need to subtract the 4x on both sides and add the 2 to both sides as well

Answer 3

so now you should have y = -4x + 2. the reason i did this is because i find it easier to know the slop when it is in this form

Answer 4

when in y = mx + b form the way we have it, the m or in your case the -4 is the slope

Answer 5

because you are looking for a line parallel to this one, it will have the same slope so we have our m

Answer 6

now, i would recommend using point slope form which is\[y-y _{1}=m(x-x _{1})\]

Answer 7

where y1 is your y coordinate and x1 is your x coordinate

Answer 8

so for (4, -3) with a slope of -4, your equation should look like \[y+3=-4(x-4)\]

Answer 9

from there, solve for y

Answer 10

i would recommend distributing the -4 first for this and then subtracting the 3

Answer 11

once youve done that you should get \[y=-4x+13\]

Answer 12

and that would be your answer