Linear functions are used to represented straight lines.
The linear function is [tex]y = -\frac 12x + 1[/tex]
The points on the graph are: (2,0) and (0,1)
Start by calculating the slope (m) using:
[tex]m = \frac{y_2 -y_1}{x_2 -x_1}[/tex]
Substitute values for x and y
[tex]m = \frac{1 - 0}{ 0 -2}[/tex]
[tex]m = \frac{1 }{ -2}[/tex]
Rewrite as:
[tex]m = -\frac{1 }{2}[/tex]
The equation is then calculated as:
[tex]y = m(x - x_1) + y_1[/tex]
This gives
[tex]y = -\frac 12(x -0) + 1[/tex]
[tex]y = -\frac 12(x) + 1[/tex]
Open bracket
[tex]y = -\frac 12x + 1[/tex]
Hence, the linear function is [tex]y = -\frac 12x + 1[/tex]
Read more about linear functions at:
https://brainly.com/question/15602982
