Question

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

(6; 5).
(1) = −6,50 + 0,50;
(2) = 0,25 − 6,50;
(3) = 6,50 − 0,25;
(4) = −0,65 − 0,25x

Answer 1

`y=6.50-0.25x`

Explanation:

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

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

`\textsf{slope}\:(m)=(y_2-y_1)/(x_2-x_1)=(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`