Question

Write in Standard form an equation of the line with the given slope through the given point.

Slope=-4;(2,2)

Answer 1

standard form for a linear equation means

• all coefficients must be integers, no fractions

• only the constant on the right-hand-side

• all variables on the left-hand-side, sorted

• "x" must not have a negative coefficient

`(\stackrel{x_1}{2}~,~\stackrel{y_1}{2})\hspace{10em} \stackrel{slope}{m} ~=~ - 4 \\\\\\ \begin{array}c \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{2}=\stackrel{m}{- 4}(x-\stackrel{x_1}{2})\implies y-2=-4x+8 \\\\\\ y=-4x+10\implies {\Large \begin{array}{llll} 4x+y=10 \end{array}}`