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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