Answer:
y = - 5x + 22
Explanation:
A linear equation has the form
y = mx + c ( m is the slope and c the y- intercept )
to obtain the equation we require to find m and c
given
f(3) = 7 , means when x = 3 then y = 7
f(1) = 17 , means when x = 1 then y = 17
substitute these values into the equation to obtain a pair of simultaneous equations
7 = 3m + c → (1)
17 = m + c → (2)
subtract (2) from (1) term by term to eliminate c
7 - 17 = (3m - m) + (c - c)
- 10 = 2m + 0
- 10 = 2m ( divide both sides by 2 )
- 5 = m
substitute m = - 5 into (1) and solve for c
7 = 3(- 5) + c
7 = - 15 + c ( add 15 to both sides )
22 = c
now substitute the values for m and c into the linear equation
y = - 5x + 22