Maths-

General

Easy

Question

# 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.

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