Question

Consider the line represented by the equation 5x + 2y = 10. How is the slope of the line related to values of A, B, and C in standard form Ax + By = C?

Analytic geometry
ANSWERED
asked 2021-02-16

Consider the line represented by the equation \(5x + 2y = 10\). How is the slope of the line related to values of A, B, and C in standard form \(Ax + By = C\)?

Answers (1)

2021-02-17

Consider the standart form of equation:
\(Ax+By=C\)
Isolate the variable y term on one side of the equation:
\(By=-Ax+c\)
Divide both sides of the equation with B to write the equation in slope intercept form:
\(\displaystyle{y}=-\frac{{A}}{{B}}{x}+\frac{{C}}{{B}}\)
This implies that the slope of an equation written in standart form is \(\displaystyle-\frac{{A}}{{B}}\), therefore the slope of \(5x+2y=10\) is \(\displaystyle-\frac{{5}}{{2}}\)

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