Chapter 4.1, Problem 33E

To determine

To write:The standard form of equation in slope and $y$ intercept of equation $-6x+5y=9$ .

Answer to Problem 33E

Slope intercept for $y=\frac{-A}{B}x+\frac{C}{B}$ .

Slope of given equation $=\frac{6}{5},y$ intercept $=\frac{9}{5}$ .

Explanation of Solution

Given Information: - We are given the standard form of a linear equation $Ax+By=C$ . Also, an equation $-6x+5y=9$ .

Calculation:

The given standard form of equation is

  $Ax+By=C$

  $By=-Ax+C$

Divide both sides by B

  $y=-\frac{A}{B}x+\frac{C}{B}$

This is the slope intercept form

slope $=\frac{-A}{B}$

  $y$ intercept $=\frac{C}{B}$

Given equation is $-6x+5y=9$

slope $=\frac{-A}{B}=\frac{-(-6)}{5}=\frac{6}{5}$

  $y$ intercept $=\frac{C}{B}$

  $=\frac{9}{5}$