Respuesta :
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 = [tex]\frac{1-6}{2-1}[/tex] = - 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:
[tex]y=-5x+11[/tex]
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:
[tex](x_1,y_1)=(1,6)\\(x_2,y_2)=(2,1)[/tex]
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 : [tex]y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]
Substitute the values
[tex]y-6=\frac{1-6}{2-1}(x-1)[/tex]
[tex]y-6=-5(x-1)[/tex]
[tex]y-6=-5x+5[/tex]
[tex]y=-5x+11[/tex]
So, Option A is true.
Hence The equation of a line that passes through the points (1,6) and (2,1) is[tex]y=-5x+11[/tex]
