Q:

A line passes through (9,-9) and (10,-5).a. Write an equation for the line in point-slope form.b. Rewrite the equation in standard form using integers.y-9 = 46% + 9); -4x + y = 45y + 9 = 4(x + 9); -4% + y = -45Y + 9 = 4(-9); -4x + y = -45y - 9 = 40%-9); -4% + y = 45

Accepted Solution

A:
[tex]\bf (\stackrel{x_1}{9}~,~\stackrel{y_1}{-9})\qquad (\stackrel{x_2}{10}~,~\stackrel{y_2}{-5}) \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{-5-(-9)}{10-9}\implies \cfrac{-5+9}{1}\implies 4 \\\\\\ \begin{array}{|c|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-(-9)=4(x-9)\implies y+9=4(x-9) \\\\\\ y+9=4x-36\implies y=4x-45\implies \stackrel{\textit{standard form}}{-4x+y=-45}[/tex]just a quick notestandard 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 coefficientnow, however the inappropriate choices here, do have it with a negative "x".