Answer:
The equation of the linear function is f(x) = -3x - 4
Step-by-step explanation:
The form of the equation of the linear function is f(x) = m x + b, where
- m is the slope of the line which represent the function
- b is the y-intercept which is value f(x) at x = 0
The rule of the slope is m = Δy/Δx, where
- Δx = x2 - x1 and Δy = y2 - y1
- (x1, y1) and (x2, y2) are two points on the line
∵ f(x) = y
∴ The coordinates of any point belongs to the function are (x, y)
∵ f(-4) = 8 and f(2) = -10
∴ The points are (-4, 8) and (2, -10)
∵ x1 = -4 and y1 = 8
∵ x2 = 2 and y2 = -10
→ Find Δx and Δy
∴ Δx = 2 - (-4) = 2 + 4 = 6
∴ Δy = -10 - 8 = -18
→ Substitute them in the rule of the slope
∵ m = [tex]\frac{-18}{6}[/tex]
∴ m = -3
→ Substitute it in the form of the equation above
∴ f(x) = -3x + b
→ To find b substitute x by -4 and f(x) by 8
∵ 8 = -3(-4) + b
∴ 8 = 12 + b
→ Subtract 12 from both sides
∵ 8 - 12 = 12 - 12 + b
∴ -4 = b
→ Substitute it in the equation
∴ f(x) = -3x + (-4)
∴ f(x) = -3x - 4
∴ The equation of the linear function is f(x) = -3x - 4
