The graph of , where m and b are constants, is shown in the xy - plane. What is the value of m ?

The correct answer is: 2

In the given graph, line y = mx + b is shown which passes through the given points-
A (0,4); B (-1,2); C (-2,0) & D (-3,-2)
Step-by-step solution:-
We know that if a point lies on a given equation then, the coordinates of that point are the solutions of that equation.
∴ we substitute the coordinates of any 2 points in the equation y = mx + b and get 2 simultaneous equations. Then we will solve the 2 simultaneous equations to find the value of m.

i. Substituting Point A (0,4)
y = mx + b
∴ 4 = m (0) + b
∴ 4 = 0 + b
∴ 4 = b
∴ b = 4 -----------------(equation i)
ii. Substituting Point C (-2,0)
y = mx + b
∴ 0 = m (-2) + b
∴ 0 = -2m + b
∴ 2m - b = 0 ----------- (Multiplying both sides with -1) ------------- (equation ii)
We get 2 equations-
2m - b = 0 and b = 4
Now, we solve these 2 equations by substituting b = 4 in 2m - b = 0
∴ 2m - b = 0
∴ 2m - 4 = 0
∴ 2m = 4
∴ m =  = 2
Final Answer:-
∴ Value of m for the given question is 2 units.