Question

Determine the linear function of the line that goes through the points (2; 6) and

Answer 1

Answer:

$y=6.50-0.25x$

Step-by-step explanation:

$\textsf{let}\:(x_1,y_1)=(2,6)$

$\textsf{let}\:(x_2,y_2)=(6,5)$

$\textsf{slope}\:(m)=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{5-6}{6-2}=-0.25$

Point-slope form of linear equation:  $y-y_1=m(x-x_1)$

(where m is the slope and (x₁, y₁) is a point on the line)

Substituting the found slope and a point on the line:

$\implies y-6=-0.25(x-2)$

$\implies y-6=-0.25x+0.5$

$\implies y=-0.25x+6.5$

Rearranging the equation to match the answer options given:

$\implies y=6.50-0.25x$