Question

Which of the following is an equation of the line through (2,3) and (-1,-12)

Answer 1

Answer:

y = 5x - 7

Step-by-step explanation:

Using the equation of a line with two points

y_2 - y_1 / x_2 - x_1 = y - y_1 / x - x_1

Giving two points

( -4 , 10)(16 , -2)

x_1 = -4

y_1 = 10

x_2 = 16

y_2 = -2

Using the above formula

y_2 - y_1 / x_2 - x_1 = y - y_1 / x - x_1

-12 - 3 / -1 - 2 = y - 3 / x - 2

-15/-3 = y - 3 /x - 2

Cross multiply

-15(x - 2) = -3(y - 3)

-15x + 30 = -3y + 9

-15x + 30 + 3y - 9 = 0

-15x +30 - 9 + 3y = 0

-15x + 21 + 3y = 0

3y = 15x - 21 ( following y = mx + C

Dividing through by 3 to find y

3y/3 = 15x -21 / 3

y = 15x - 21 / 3

We can still separate

y = 15x / 3 - 21/3

y = 5x - 7

Therefore, the equation of the line is

y = 5x - 7