Answer:
[tex]y = - \frac{1}{2} x + 2[/tex]
Step-by-step explanation:
According to the chart for the values of x (input) the corresponding values of y (output) are given.
The slope of the equation is constant and given by [tex]m = - \frac{1}{2}[/tex].
If we want to check the slope to be constant then we can use the table and the values of x and y.
The first point ([tex]x_{1},y_{1}[/tex]) ≡ (-2,3)
The second point ([tex]x_{2},y_{2}[/tex]) ≡ (8,-2)
The third point ([tex]x_{3},y_{3}[/tex]) ≡ (10,-3)
The fourth point ([tex]x_{4},y_{4}[/tex]) ≡ (20,-8)
Now, we can check that slope of the straight line is constant for all those values.
[tex]\frac{y_{2} - y_{1}}{x_{2} - x_{1}} = \frac{- 2 - 3}{8 - (- 2)} = - \frac{1}{2}[/tex]
[tex]\frac{y_{3} - y_{2}}{x_{3} - x_{2}} = \frac{- 3 - (- 2)}{10 - 8} = - \frac{1}{2}[/tex]
[tex]\frac{y_{4} - y_{3}}{x_{4} - x_{3}} = \frac{- 8 - (- 3)}{20 - 10} = - \frac{1}{2}[/tex]
Now, Let us assume that the equation of the straight line is [tex]y = - \frac{1}{2} x + c[/tex] ....... (1)
Now, we have to find the value of c.
This straight line passes through ([tex]x_{1},y_{1}[/tex]) ≡ (-2,3) point.
So, the value of c can be calculated from the equation (1) as, c = 3 - 1 = 2
Therefore, [tex]y = - \frac{1}{2} x + 2[/tex] is the required equation. (Answer)
