Question

Pls help asap!!!!!!!!!

Answer 1

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 = $\frac{-18}{6}$

∴ 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