Question

write the equation in standard form of a line that passes through the point (4,-2) and has a slope of -1

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