What is the y-intercept of (-10,-4) (-1,2)

Question

I need to find a line passes through the points (-10,-4) (-1,2) which is the y-intercept of the line?

1. (0,8/3)

2. (9/3,0)

3.(0,-4)

4. (-4,0)

Answer 1

Line equation is

Cross multiplication

9y+36 = 6x+60

Subtract 36 from each side.

9y = 6x+24

Divide to each side by 9.

y = (2/3)x+8/3.

y intercept is 8/3.

Option 1 is correct choice.

Answer 2

The points are (- 10, - 4) and (- 1, 2).

Slope - intercept - form of a line equation is y = mx + c, where, m is slope and c is y - intercept.

Slope (m ) = (y ₂ - y ₁)/(x ₂ -x ₁).

Substitute the values of (x ₁, y ₁) = (- 10, - 4) and (x ₂, y ₂) = (- 1, 2) in m = (y ₂ - y ₁)/(x ₂ -x ₁).

m = (2 -  (- 4)) / (- 1 - (- 10))

m = (2 + 4)/(- 1 + 10)

m = 6/9

⇒ m = 2/3.

Substitute the values of m = 2/3 and (x, y ) = (- 10, - 4) in slope - intercept - form of a line equation : y = mx + c.

- 4 = (2/3)(- 10) + c

- 4 = - 20/3 + c

⇒ c = - 4 + 20/3 = (- 12 + 20)/3 = 8/3.

Therefore, y - intercept of the points (- 10, - 4) and (- 1, 2) is (0, 8/3).

The correct choice is option 1.