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

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. 

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

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.

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

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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