Question

Write an equation in standard form of the line passing through points

Answer 1

`\bf \cfrac{\quad (36-20)/(45)\quad }{(54+20)/(45)}\implies \cfrac{\quad(16)/(45) \quad }{(74)/(45)}\implies \cfrac{16}{45}\cdot \cfrac{45}{74}\implies \cfrac{16}{74}\implies \cfrac{8}{37} \\\\\\ % point-slope intercept \stackrel{\textit{point-slope form}}{y- y_1= m(x- x_1)}\implies y-\cfrac{4}{9}=\cfrac{8}{37}\left[ x -\left( -\cfrac{4}{9} \right)\right]`


`\bf y-\cfrac{4}{9}=\cfrac{8}{37}\left( x +\cfrac{4}{9} \right)\implies y-\cfrac{4}{9}=\cfrac{8}{37}x+\cfrac{32}{333} \\\\\\ y=\cfrac{8}{37}x+\cfrac{32}{333}+\cfrac{4}{9}\implies y=\cfrac{8}{37}x+\cfrac{32}{333}+\cfrac{148}{333}\implies y=\cfrac{8}{37}x+\cfrac{180}{333} \\\\\\ y=\cfrac{8}{37}x+\cfrac{20}{37}\implies \stackrel{standard~form}{-\cfrac{8}{37}x+y=\cfrac{20}{37}}`