Question

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.​

Answer 1

`\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}{10-9}\implies \cfrac{4}{1}\implies 4 \\\\\\ \begin{array} \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)`

now, bearing in mind that 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

`\bf y+9=4(x-9)\implies y+9=4x-36\implies y=4x-45 \\\\\\ -4x+y=-45\implies \stackrel{\textit{standard form}}{4x-y=45}`