Question

The diagram below shows a sketch of part of the graph y = ax+ bx + 3.

The two points V and W each lie on the graph and have co-ordinates (-1,10) and (2.13).
W
(2,13)
V
(-1,10)
Diagram is
NOT to scale
Find the values of the numbers a and b.

Answer 1

Explanation:

There appears to be a problem with your equation as it can be reduced to

y = (a + b)x + 3

which is a line of slope (a + b) and y intercept of 3

plugging in our points

10 = -1(a + b) + 3

7 = -1(a + b)

a + b = -7

13 = 2(a + b) + 3

10 = 2(a + b)

a + b = 5

a + b cannot equal both 5 and -7 at the same time.

I will GUESS that you mean y = ax² + bx + 3

10 = a(-1)² + b(-1) + 3

10 = a - b + 3.

b = a - 7

13 = a(2)² + b(2) + 3

13 = 4a + 2b + 3

10 = 4a + 2b

10 = 4a + 2(a - 7)

10 = 4a + 2a - 14

24 = 6a

a = 4

b = 4 - 7

b = -3