x- and y-Intercepts

x- and y-Intercepts

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The graphical concept of x- and y-intercepts is pretty simple. The x-intercepts are where the graph crosses the x-axis, and the y-intercepts are where the graph crosses the y-axis. The problems start when we try to deal with intercepts algebraically.
To clarify the algebraic part, think again about the axes. When you were first introduced to the Cartesian plane, you were shown the regular number line from elementary school (the x-axis), and then shown how you could draw a perpendicular number line (the y-axis) through the zero point on the first number line. Take a closer look, and you'll see that the y-axis is also the line "x = 0". In the same way, the x-axis is also the line "y = 0".
Then, algebraically,

• an x-intercept is a point on the graph where y is zero, and
• a y-intercept is a point on the graph where x is zero.

More specifically,

• an x-intercept is a point in the equation where the y-value is zero, and
• a y-intercept is a point in the equation where the x-value is zero.
     

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• Find the x- and y-intercepts of 25x² + 4y² = 9

Using the definitions of the intercepts, I will proceed as follows:
x-intercept(s):

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 are the points ( ³/₅, 0) and ( ^–3/₅, 0)
y-intercept(s):   Copyright © Elizabeth Stapel 1999-2011 All Rights Reserved

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 are the points (0, ³/₂ ) and (0, ^–3/₂ )

Just remember: Whichever intercept you're looking for, the other variable gets set to zero.