Question

Find the equation of the linear function x 1 2 3 4 y 6 9 12 15​

Answer 1

Answer:

The equation of the linear function is y = 3x + 3

Step-by-step explanation:

The form of the linear equation is y = m x + b, where

• m is the slope

• b is the y-intercept

The rule of the slope is m = $\frac{y2-y1}{x2-x1}$ , where

• (x1, y1) and (x2, y2) are two points on the line

∵ A line passes through points (1, 6) and (2, 9)

∴ x1 = 1 ad y1 = 6

∴ x2 = 2 and y2 = 9

→ Use the rule of the slope above to find the slope of the line

∵ m = $\frac{9-6}{2-1}$ = $\frac{3}{1}$ = 3

∴ m = 3

→ Substitute the value of m in the form of the equation above

∴ y = 3x + b

→ To find b substitute x and y in the equation by the coordinates of any

   point on the line

∵ x = 1 and y = 6

∴ 6 = 3 (1) + b

∴ 6 = 3 + b

→ Subtract 3 from both sides

∵ 6 - 3 = 3 - 3 + b

∴ 3 = b

→ Substitute the value of b in the equation above

∴ y = 3x + 3

∴ The equation of the linear function is y = 3x + 3