Answer:
[tex]y = -2x[/tex]
Step-by-step explanation:
Given
x || 0 || 1 || -2
y || 0 || -2 || 4
Required
Determine the function rule
First, we have to determine the slope of the function using;
[tex]m = \frac{y_1 - y_2}{x_1 - x_2}[/tex]
Where x and y represent any two corresponding values of x and y
When x = 0; y = 0 [tex](x_1,y_1)[/tex]
When x = 1; y = -2 [tex](x_2,y_2)[/tex]
Substitute these values in [tex]m = \frac{y_1 - y_2}{x_1 - x_2}[/tex]
[tex]m = \frac{0 - (-2)}{0 - 1}[/tex]
[tex]m = \frac{0 +2}{0 - 1}[/tex]
[tex]m = \frac{2}{- 1}[/tex]
[tex]m = -2[/tex]
Next, is to determine the function rule; using slope intercept form as follows;
[tex]y - y_1 = m(x - x_1)[/tex]
Take any corresponding values of x and y as x1 and x2
When x = -2; y = 4
[tex]y - y_1 = m(x - x_1)[/tex] becomes
[tex]y - 4 = -2(x - (-2))[/tex]
[tex]y - 4 = -2(x + 2)[/tex]
Open the bracket
[tex]y - 4 = -2x -4[/tex]
Add 4 to both sides
[tex]y - 4 + 4 = -2x - 4 + 4[/tex]
[tex]y = -2x[/tex]
Hence, the function rule is [tex]y = -2x[/tex]
