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
The rule of the slope is m = [tex]\frac{y2-y1}{x2-x1}[/tex] , 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 = [tex]\frac{9-6}{2-1}[/tex] = [tex]\frac{3}{1}[/tex] = 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
