Answer:
The equation of the line or linear function is:
y = -2x
Step-by-step explanation:
Given the table
x 3 6 9 12
y -6 -12 -18 -24
As there is a constant change in x and y values, so the table represents the linear function.
The slope-intercept form of the linear equation
y = mx+b
where
Taking any two points, let say
Determining the slope between (3, -6) and (6, -12)
[tex]\mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]m=\frac{-12-\left(-6\right)}{6-3}[/tex]
Refine
[tex]m=-2[/tex]
Thus, the slope m = -2
now substituting m = -2 and (3, -6) in the slope-intercept form
y = mx+b
-6 = -2(3) +b
-6 = -6 + b
b = -6 + 6
b = 0
Thus, the y-intercept b = 0
now substituting m = -2 and b = 0 in the slope-intercept form of linear function
y = mx+b
y = -2x + 0
y = -2x
Therefore, the equation of line or linear function is:
y = -2x
