The y-intercept is where the line (or curve) crosses the y-axis.  Mathematically, if you have y = some_function_of_x  then it is the y value when you set x=0.





OPTIONAL:

For example, when dealing with straight lines, the equation of the line is often written y = mx + b   where m=slope (the rise/run or  (change in y) / (change in x)) and b is the y-intercept.   



Below is the graph of  y = 2x-5 in green.  Notice how the line meets the y-axis at -5:



 

Answer by Cromlix(4381)   (Show Source): You can put this solution on YOUR website!
 Hi there,

The equation of a line is y = mx + c

m = gradient or slope

c = the line's y intercept 



Knowing the line's y intercept allows, with the x intercept, to work out the gradient or slope.

e.g. y = 4x + 8

To find where the line cuts the x axis make y = 0 

0 = 4x + 8

4x = -8

x = -2     Cuts x axis at (-2, 0)

To find where line cuts the y axis make x = 0

y = 4x + 8

y = 4(0) + 8

y = 8   cuts y axis at (0, 8)

To find the gradient use y2 - y1/x2 - x1

Using the example y = 4x + 8, the y intercept (0, 8) (x1, y1) and the x intercept (-2, 0)  (x2, y2)

y2 - y1/x2 - x1  = 0 - 8/-2 - 0  = -8/-2 = 4 The gradient (slope) in y = 4x + 8

Hope this helps, mate. :-) 

Answer by Theo(13342)   (Show Source): You can put this solution on YOUR website!
 the y-intercept is the value of y when the value of x is equal to 0.





it is helpful to know what specific problems your son is having difficulty with, as the answer to the meaning of the y-intercept depends on the nature of the problem.





the most common usage for young children just starting in algebra is in solving straight line equations.





more specifically, the slope intercept form of the equation of the line is used.





the child is given two points or one point and a slope and the child needs to determine what the equation is.





here's a reference that might be helpful.





https://www.purplemath.com/modules/slopyint.htm





here's a reference on how to interpret and solve word problems.





https://www.purplemath.com/modules/translat.htm





here's the second page of that reference.





https://www.purplemath.com/modules/translat2.htm





here's some problems that involve the use of the slope intercept form of the equation of a straight line.





https://fathersoninnovations.com/wp-content/uploads/2018/06/Slope-Intercept-Form-Word-Problems.pdf





here's a tutorial on how to derive the slope intercept form of the equation of a straight line.





https://www.mathsisfun.com/equation_of_line.html





here's another reference on how to find the equation of a straight line, given certain attributes of the line.





https://www.purplemath.com/modules/strtlneq.htm





your question is very general.

it helps to understand the question in terms of the specific problem your son is dealing with.





going through a couple of examples can help to determine how the y-intercept is used to solve those problems.





web searches such as i did to find some references can also be helpful.





youtube also has lots of tutorials that can also be helpful.







 

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