Answer:
The equation is y = 3x + 2
Step-by-step explanation:
The form of the linear equation is y = m x + b, where
- m is the slope of the line which represent the equation
- b is the y-intercept which is value y 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.
∵ x is the input
∵ Input: 0, 1, 2, 3, 4
∵ y is the output
∵ output: 2, 5, 8, 11, 14
∴ The points on the line are (0, 2), (1, 5), (2, 8), (3, 11), and (4, 14)
→ Use any two points to find m
∵ x1 = 0 and y1 = 2
∵ x2 = 1 and y2 = 5
→ Find Δx and Δy
∴ Δx = 1 - 0 = 1
∴ Δy = 5 - 2 = 3
→ Substitute them in the rule of the slope above
∵ m = [tex]\frac{3}{1}[/tex]
∴ m = 3
∵ b is the value of y at x = 0
∵ At x = 0, y = 2
∴ b = 2
→ Substitute the values of m and b in the form of the equation above
∵ y = 3x + 2
∴ The equation is y = 3x + 2
