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What is the relation between intercepts and the constant term in the standard form?
Example Solution: 2x+3y=6
The standard form of a linear equation is written as: Ax+By=C. When we want to find the x-intercept, we substitute y with 0 and solve for x.
Therefore, the x- and y-intercepts of any line written in standard form are: x=C/A and y=C/B. Here we notice that in order to have integer values for intercepts we need to choose a value for C such that it is divisible by both A and B. The simplest case will be: C=A * B. This number is a multiple of A and B and will therefore be divisible by both of those coefficients. Now we have the equation in the form of Ax+By=AB. Let's choose A=2 and B=3 and substitute this into the formula above.