A linear equation's graph moves through ( -2,0) and&nbsp;(0,-6) is the&nbsp;3x−y=6, both ordered pairs solutions for the equation

3x−y=6 (1) We know that the equatioan passing through (x1,y1)and(x2,y2) is y−y1=y2−y1x2−x1(x−x1) y−0=−6−00−(−2)(x−(−2)) y=−62(x+2) y=−3(x+2) y=−3x−6 3x+y+6=0 3x+y=−6(2) By, equations (1)+(2), we get 3x−y=6 3x+y=−6 6x=0⇒x=0 put value in equation (2), we get 3x+y=−6 3×0+y=−6 y=−6 So, ordered parts (0,-6)

Step by step solution to "A linear equation's graph moves through ( -2,0)..."

High School
Algebra
Algebra I
Linear equations and graphs

Daniaal Sanchez

Answered question

2020-12-03

A linear equation's graph moves through ( -2,0) and (0,-6) is the $3 x - y = 6$ , both ordered pairs solutions for the equation

Answer & Explanation

lobeflepnoumni

Skilled2020-12-04Added 99 answers

$3 x - y = 6$ (1)
We know that the equatioan passing through $(x_{1}, y_{1}) a n d (x_{2}, y_{2})$ is
$y - y_{1} = \frac{y_{2} - y_{1}}{x_{2} - x_{1}} (x - x_{1})$
$y - 0 = \frac{- 6 - 0}{0 - (- 2)} (x - (- 2))$
$y = - \frac{6}{2} (x + 2)$
$y = - 3 (x + 2)$
$y = - 3 x - 6$
$3 x + y + 6 = 0$
$3 x + y = - 6 (2)$
By, equations $(1) + (2)$ , we get
$3 x - y = 6$
$3 x + y = - 6$
$6 x = 0 \Rightarrow x = 0$
put value in equation (2), we get
$3 x + y = - 6$
$3 \times 0 + y = - 6$
$y = - 6$
So, ordered parts (0,-6)

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