The point slope form of the equation of the line that passes through (-5,-1) and (10,-7) is y+7=-2/5(x-10). what is the standard form of the equation for this line?

a. 2x-5y=-15
b. 2x-5y=-17
c. 2x+5y=-15
d. 2x+5y=-17

Option C

The standard form of the equation for y + 7 = -2/5(x - 10) is 2x + 5y = -15.

Solution:

Need to determine standard form of equation of line passing through points (-5, -1) and (10, -7) and having slope form as  

Standard form of equation of line is such that terms having variables are on left hand side and constant terms on right hand side.

So let’s simplify given slope form.

On opening the brackets we get

=> 5(y + 7) = -2x +20

=> 5y + 2x = 20 – 35

=> 2x +5y = -15

Hence the standard form is 2x + 5y = -15.

let's cover over the formula of the vertex:

y = a(x – h)^2 + k

in this formula, (h,k) are the vertex, always remember that the positive or negative value of the vertex is based on the sign it has.

for example, if the vertex is -3,-6 then both the x and y value would have the positive sign attached to it and if it were a positive x and y value, then a negative sign would be attached to it.

with that being said, for our problem the x value is a positive one so we are looking for a number with a negative sign next to it, in this case the first and second choice.

however, for the first answer choice it isn't quite part of the formula so we know that the answer choice correctly displays the x value.

to confirm, we can see if the -1 fits correctly with the second answer choice, and as mentioned above a negative number will have a positive sign attached to it. so, for our problem we can see that -1 has been changed to +1, so we can confirm that the second answer choice is correct.

hence, our final answer is y=(x - 1)^2 + 1

hello from mrbilldoesmath!

answer:

25x^2 + 90x + 84

discussion:

mn(x) = m(n(x)) = m( 5x + 9) =

(5x + 9)^2 + 3 =>

25x^2 + 90x + 9^2 + 3 =

25x^2 + 90x + 84                 (as 9^2 = 9*9 = 81)

which is the second choice

regards,  

mrb

p.s.   i'll be on vacation from friday, dec 22 to jan 2, 2019. have a great new year!