Answer:
[tex]y = -\frac{1}{2}x + 2[/tex]
Step-by-step explanation:
Assume this is function is a straight line, consider the equation of the straight line: [tex]y=mx + c[/tex]
To find the gradient of the equation, we use any two coordinates from the table. [tex](x_1,y_1) = (6,-1)\\(x_2,y_2) =(2,1)[/tex]
[tex]m = \frac{y_1 - y_2}{x_1 - x_2}\\\\m = \frac{1-(-1)}{2-6}\\\\m=\frac{2}{-4} \\\\m=- \frac{1}{2}[/tex]
We substitute the value of m in the equation:
[tex]y =mx+c\\y = - \frac{1}{2} x + c\\\\[/tex]
To find c, we use the leftover coordinates, (4,0) in the equation above:
[tex]y = -\frac{1}{2}x+c\\\\0 = -\frac{1}{2} \times 4+c\\\\0 = -2 + c\\\\c=2\\\\[/tex]
Substitute this value of c in the equation to get the function:
[tex]y = -\frac{1}{2}x + 2[/tex]
