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. y + 9 = 4(x – 9); –4x + y = –45 y – 9 = 4(x + 9); –4x + y = 45 y – 9 = 4(x – 9); –4x + y = 45 y + 9 = 4(x + 9); –4x + y = –45

Answer 1

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 (\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`

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

Answer 2

y+9=4(x-9);-4x+y=-45