Question

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

2x – 5y = –15
2x – 5y = –17
2x + 5y = –15
2x + 5y = –17

Answer 1

Hello
the standard form of the equation for this line is : 2x + 5y = –15
because :
2(-5)+5(-1) = -15
2(10)+5(-7) = -15

Answer 2

Option C. 2x + 5y = -15

Explanation:

A line which passes through two points (-5, -1) and (10, -7) will have the slope = (y - y')/(x - x') = (-1 + 7)/(-10 - 5) = 6/(-15) = (-2/5)

Now the equation will be y = (-2/5)x + c

Since this line passes through (10, -7) therefore the equation of the line will be

-7 = (-2/5)(10) + c

-7 = -4 + c

c = -7 + 4 = -3

Then the final equation of the line will be

y = (-2/5)x - 3

Multiplying with 5 on both the sides of the equation

5y = (-2/5)×5 - 3×5

5y = -2x - 15

2x + 5y = -15

Therefore option C is the answer.