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Question

The graph of the line y=mx+b is given by some random points. What is the slope and intercept of the line?


A
m=2, b=3
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B
m=2, b=3
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C
m=2, b=3
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D
m=2, b=3
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Solution

The correct option is A m=2, b=3
Given Line: y=mx+b,
where m= slope, b= intercept.

Slope=rate of change of yrate of change of x =rise/fallrun

How to check graph is falling or rising:
  • When x is increasing and y is also increasing then graph is rising.
  • When x is increasing and y is decreasing then graph is falling.
From the above graph,
x=1,y=5
x=0,y=3
x=1,y=1
x=2,y=1
Here, x value is increasing and y value is decreasing continuously. So, this graph is falling.

Find rise/fallrun:
Here, line intersect y axis at (0,3). So, y value is 3.
Since, graph is falling, hence y value will be negative.
So, fall =3

Here, graph intersect x axis at (1.5,0). x value will be 1.5.
Hence, run =1.50=1.5

So, slope m=fallrun
=31.5
=2

How to find intercept from graph:
y is the intercept of the given line.
Here, graph intersect y axis at (0,3). So, y value is 3. Hence intercept is 3.

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