A graph of a linear equation passes through ( -2,0) & (0,-6) is the 3x-y=6, both ordered pairs solutions for the equation

A graph of a linear equation passes through ( -2,0) & (0,-6) is the 3x-y=6, both ordered pairs solutions for the equation

Question
Linear equations and graphs
asked 2020-12-03

A graph of a linear equation passes through ( -2,0) and (0,-6) is the \(3x-y=6\), both ordered pairs solutions for the equation

Answers (1)

2020-12-04

\(3x-y=6\) (1)
We know that the equatioan passing through \((x_1,y_1) and (x_2,y_2)\) is
\(\displaystyle{y}-{y}_{{1}}=\frac{{{y}_{{2}}-{y}_{{1}}}}{{{x}_{{2}}-{x}_{{1}}}}{\left({x}-{x}_{{1}}\right)}\)
\(\displaystyle{y}-{0}=\frac{{-{6}-{0}}}{{{0}-{\left(-{2}\right)}}}{\left({x}-{\left(-{2}\right)}\right)}\)
\(\displaystyle{y}=-\frac{{6}}{{2}}{\left({x}+{2}\right)}\)
\(\displaystyle{y}=-{3}{\left({x}+{2}\right)}\)
\(\displaystyle{y}=-{3}{x}-{6}\)
\(\displaystyle{3}{x}+{y}+{6}={0}\)
\(\displaystyle{3}{x}+{y}=-{6}{\left({2}\right)}\)
By, equations \((1) + (2)\), we get
\(\displaystyle{3}{x}-{y}={6}\)
\(\displaystyle{3}{x}+{y}=-{6}\)
\(\displaystyle{6}{x}={0}\Rightarrow{x}={0}\)
put value in equation (2), we get
\(\displaystyle{3}{x}+{y}=-{6}\)
\(\displaystyle{3}\times{0}+{y}=-{6}\)
\(\displaystyle{y}=-{6}\)
So, ordered parts (0,-6)

0

Relevant Questions

asked 2021-02-09

What is the process to solve these:
Vertex, \(y-\int\)., \(x-\int\), graph \(= -(x+1)^2+1\)

asked 2020-10-26

Determine the value of k for which the point (- 2, 3) lies on the line whose equation is .

\(4x+3ky=10\)

asked 2021-01-02

Solve linear equation and check: \(7x+3=6(x-1)+9\)

asked 2020-12-13

A system of linear equations is a set of two or more equations taken together. The point where the two graphs intersect is called the solution.
\(\displaystyle{\left\lbrace\begin{array}{c} {y}=\frac{{1}}{{3}}{x}-{3}\\{y}=-{x}+{1}\end{array}\right.}\)
a) Complete the table fo each linear function
image
b) Graph both equations on the coordinate plane below

asked 2021-03-18

Describe the relationship between the two quantities.

asked 2021-01-31

Simplify each expression.
1) \(-n+9n+3-8-8n\)
2) \(3(-4x+5y)-3x(2+4)\)
3) \(5-4y+x+9y\)
4) \(-2x+3y-5x-(-8y)\)

asked 2021-02-19

\(y = -3x - 13\) and \(4x + 3y = - 24\)

asked 2021-02-22

How to complete the table with the equation \(y=10x-4\)

asked 2020-10-23

Determine whether the ordered pair is a solution to the given system of linear equations.
(1,2)
\(\left\{\begin{matrix} 3x−y=1 \\ 2x+3y=8 \end{matrix}\right\}\)

asked 2021-03-12

Determine whether the ordered pair is a solution to the given system of linear equations.
(5,3)
\(x-y=2\)
\(x+y=8\)

...