Index that lessonsPrint this page (print-friendly version) | find local tutors
x- and y-Intercepts
The graphical ide of x- and y-intercepts is quite simple. The x-intercepts room where the graph crosses the x-axis, and the y-intercepts space where the graph the cross the y-axis. The troubles start once we shot to attend to intercepts algebraically.
You are watching: What is x=0 on a graph
To clarify the algebraic part, think again around the axes. Once you were first introduced come the Cartesian plane, friend were displayed the regular number heat from elementary college (the x-axis), and also then shown how you could draw a perpendicular number line (the y-axis) v the zero point on the very first number line. Take it a closer look, and also you"ll view that the y-axis is also the line "x = 0". In the very same way, the x-axis is additionally the line "y = 0".
Then, algebraically, one x-intercept is a suggest on the graph wherein y is zero, and a y-intercept is a point on the graph whereby x is zero. more specifically, one x-intercept is a point in the equation wherein the y-value is zero, and also a y-intercept is a point in the equation where the x-value is zero.
See more: Mercedes-Benz E320 Transmission Fluid Change Kit, Mercedes E320 Atf Transmission Fluid Change Kit
uncover the x- and also y-intercepts the 25x2 + 4y2 = 9 making use of the meanings of the intercepts, i will continue as follows:
y = 0 for the x-intercept(s), so:
25x2 + 4y2 = 9 25x2 + 4(0)2 = 9 25x2 + 0 = 9 x2 = 9/25 x = ± ( 3/5 )
Then the x-intercepts space the point out ( 3/5, 0) and ( –3/5, 0)
x = 0 for the y-intercept(s), so:
25x2 + 4y2 = 9 25(0)2 + 4y2 = 9 0 + 4y2 = 9 y2 = 9/4 y = ± ( 3/2 )
Then the y-intercepts room the point out (0, 3/2 ) and (0, –3/2 )
Just remember: Whichever intercept you"re looking for, the various other variable gets set to zero.
In enhancement to the over considerations, you must think that the adhering to terms interchangeably:
"x-intercepts" = "roots" = "solutions" = "zeroes"
In other words, the following exercises room equivalent: uncover the x-intercept(s) that y = x3 + 2x2 – x – 3 deal with x3 + 2x2 – x - 3 = 0 find the zeroes / roots of f(x) = x3 + 2x2 – x – 3 If you keep this equivalence in the earlier of her head, countless exercises will make a lot an ext sense. For instance, if they offer you something choose the adhering to graph:
...and ask friend to find the "solutions", you"ll recognize that they mean "find the x-intercepts", and also you"ll be able to answer the question, even though they to be clumsy in their usage of the mathematical terms, and also they never provided you the equation.
Top | return to Index
Cite this write-up as:
Stapel, Elizabeth. "x- and y-Intercepts." 6294.org. Easily accessible from https://www.6294.org/modules/intrcept.htm. Accessed