Finding the x and yintercepts of an equation are important skills you'll need in math and the sciences. For some problems, this may be more complicated; fortunately, for linear equations it just couldn't be simpler. A linear equation will only ever have, at most, one xintercept and one yintercept.
XIntercept

A linear equation has the form y = mx + b, where M and B are constants. The xintercept is the point where the line crosses the xaxis. By definition, the yvalue of a linear equation when it crosses the xaxis will always be 0, since the xaxis is stationed at y = 0 on a graph. Consequently, to find a yintercept, just substitute 0 for y and solve for x. This will give you the value of x at the xintercept.
YIntercept

The yintercept is the point at which the line crosses the yaxis; the value of x must be 0 at the yintercept, because the yaxis is stationed at x = 0 on the graph. Consequently, to find the yintercept, substitute 0 for x in your equation and calculate y. For equations of the form y = mx + b, this is especially easy; if x = 0, the first term (m times x) will be 0, so y will equal b. Thus, the constant b in a linear equation is the value of y at the yintercept, while the constant m is the slope of the line  the larger m is, the steeper the slope.
Equations without Intercepts

Some equations do not have x or yintercepts; this usually happens when x or y are constant. For example, the equation y = 5 does not and cannot have an xintercept, since y will never be equal to 0. Similarly, the equation x = 5 does not have a yintercept as x will never be equal to 0. Both of these types of equations are flat lines that have no slope; the first one is perfectly horizontal, while the other is perfectly vertical.
Example

Here's an example to illustrate how you can find x and yintercepts.
Example: Fine the x and yintercepts of the equation y = 10x  12
To find the xintercept, substitute y = 0 then solve.
0 = 10x  12
12 = 10x
x = 12 / 10 = 6/5. (or 1.2)
Therefore, the xintercept is 6/5. Since this equation is in the form y = mx + b, and b is the value of y at the yintercept, you also know the yintercept must be 12.
References
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