Question

Which of the following is the equation of a line that passes through the points (1,6) and (2,1)

A. Y=-5x+11
B. Y=-5x+1
C. Y=2x+1
D. Y=5x-1

Answer 1

A

Explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

To calculate m use the slope formula

m = ( y₂ - y₁ ) / ( x₂ - x₁ )

with (x₁, y₁ ) = (1, 6) and (x₂, y₂ ) = (2, 1)

m =
`(1-6)/(2-1)` = - 5, hence

y = - 5x + c ← is the partial equation

To find c substitute either of the 2 points into the partial equation

Using (1, 6), then

6 = - 5 + c ⇒ c = 6 + 5 = 11

y = - 5x + 11 → A

Answer 2

`y=-5x+11`

Explanation:

Given : Points (1,6) and (2,1)

To Find : Which of the following is the equation of a line that passes through the points (1,6) and (2,1) ?

Solution:

`(x_1,y_1)=(1,6)\\(x_2,y_2)=(2,1)`

Now to find the equation of a line that passes through the points (1,6) and (2,1) we will use two point slope form

Two point slope form :
`y-y_1=(y_2-y_1)/(x_2-x_1)(x-x_1)`

Substitute the values

`y-6=(1-6)/(2-1)(x-1)`

`y-6=-5(x-1)`

`y-6=-5x+5`

`y=-5x+11`

So, Option A is true.

Hence The equation of a line that passes through the points (1,6) and (2,1) is
`y=-5x+11`