160k views
1 vote
A line passes through (9, –9) and (10, –5).Write an equation for the line in point-slope form.

Rewrite the equation in standard form using integers.

A) y + 9 = 4(x + 9) ; -4x + y = -45
B) y - 9 = 4(x + 9) ; -4x + y = 45
C) y - 9 = 4(x + 9) ; -4x + y = -45
D) y + 9 = 4(x + 9) ; -4x + y = 45

^^ The options look pretty similar, so please make sure you're answering correctly! Thank you :)

User Siannone
by
7.9k points

1 Answer

0 votes

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}{1}\implies \cfrac{4}{1}\implies 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-(-9)=4(x-9)\implies\underline{y+9=4(x-9)} \\\\\\ y+9=4x-36\implies y=4x-45\implies \stackrel{standard~form}{\underline{-4x+y=-45}}

quick note:

the "x" must not have a negative coefficient for the standard form, though in this case it shows like so in the inappropriate choices above.

User Gil Pinsky
by
8.7k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories