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

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 $$Ax + By = C$$?

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 $$\displaystyle-\frac{{5}}{{2}}$$