Answer:
The values of a , b , c are ⇒ a = 1 , b = 10 , c = 9
Explanation:
* Lets describe the meaning of the linear function
- Linear function is represented by a line graphically
- The equation of the line is y = mx + c, where m is the slope
of the line and c is the y-intercept (the point of intersection
between the line and the y-axis is (0 , c))
- m = change of y/change of x
- We can find m from any two points on the line
* Lets use m to find a, b and c
- Use the points (3 , 8) and (5 , 9) to find m
∵ m = (y2 - y1)/(x2 - x1)
∴ m = (9 - 8)/(5 - 3) = 1/2
- Find a by using points (a , 7) and (3 , 8) ⇒ (or (5 , 9))
∵ m = (8 - 7)/(3 - a) = 1/2
∴ 1/(3 - a) = 1/2 ⇒ by using cross multiplication
∴ 3 - a = 2 ⇒ subtract 3 from both sides
∴ -a = -1 ⇒ × -1 both sides
∴ a = 1
- Find b by using points (5 , 9) and (7 , b) ⇒ (or (3 , 8))
∵ m = (b - 9)/(7 - 5) = (b - 9)/2
∴ (b - 9)/2 = 1/2 ⇒ by using cross multiplication
∴ 2(b - 9) = 2 ⇒ open the bracket
∴ 2b - 18 = 2 ⇒ add 18 to both sides
∴ 2b = 20 ⇒ ÷ 2
∴ b = 10
- Find b by using points (5 , 9) and (c , 11) ⇒ (or (3 , 8))
∵ m = (11 - 9)/(c - 5) = 2/(c - 5)
∴ 2/(c - 5) = 1/2 ⇒ by using cross multiplication
∴ c - 5 = 4 ⇒ add 5 to both sides
∴ c = 9
* The values of a , b , c are ⇒ a = 1 , b = 10 , c = 9