y-intercept of the Graph of y = mx + c

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Here we will learn how to find
the y-intercept of the graph of y = mx + c.

If the graph of y = mx + c cuts the y-axis at P then OP is
the y-intercept of the graph, where O is the origin. If OP is in the positive
direction of the y-axis, the intercept is positive. But if OP is in the
negative direction of the y-axis, the intercept is negative.

 As the graph of y = mx + c has a point (0, c) on it, OA = c. Thus,

the y-intercept of the line which is the graph of y = mx + c is c


Solved example on y-intercept of the graph of y = mx + c:

What is the y-intercept of the graph of 7x + 2y = 3?

Solution:

Here, 7x + 2y = 3

⟹ 2y = -7x + 3

⟹ y = – (frac{7}{2})x + (frac{3}{2})

Comparing with y = mx + c, we get c = (frac{3}{2}).
So, the y-intercept = (frac{3}{2})

Note:

By putting x = 0 in y = mx + c, we get y = c = y-intercept. So,
the y-intercept of ax + by + c= 0 can be obtained by putting x =0 in it which
gives y = (frac{-c}{b}) = y-intercept.

 

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9th Grade Math

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