Big Ideas Math Integrated I, 2016
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Big Ideas Math Integrated I, 2016 View details
4. Graphing Linear Equations in Standard Form
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Exercise 36 Page 134

What is the relation between intercepts and the constant term in the standard form?

Example Solution: 2x+3y=6

Practice makes perfect

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.

Ax+By=C
Ax+B * 0=C
â–¼
Solve for x
Ax=C
x=C/A
Similarly, finding the y-intercept means we have to substitute x with 0 and solve for y.

Ax+By=C
A* 0+By=C
â–¼
Solve for y
By=C
y=C/B

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.

Ax+By=AB
2x+ 3y= 2* 3
2x+3y=6