Question

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

Answer 1

Answer:

A

Step-by-step 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 = $\frac{1-6}{2-1}$ = - 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

Answer:

$y=-5x+11$

Step-by-step 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 : $y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)$

Substitute the values

$y-6=\frac{1-6}{2-1}(x-1)$

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

$y-6=-5x+5$

$y=-5x+11$

So, Option A is true.

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