The linear equation passing through given points is: x-3y=5
Further explanation:
We have to find the equation of line that will pass through the given points. That equation of line will be the required linear equation.
Given
(x1,y1)=(-6,-7)
(x2,y2)=(3,-4)
WE have to find the slope first
[tex]m=\frac{y_2-y_1}{x_2-x_1}\\=\frac{-4-(-7)}{3-(-6)}\\=\frac{-4+7}{3+6}\\=\frac{3}{9}\\=\frac{1}{3}[/tex]
The slope-intercept form of line is:
[tex]y=mx+b\\Putting\ the\ value\ of\ slope\\y=\frac{1}{3}x+b[/tex]
To find the value of b we have to put any one point in the equation,
So putting (3,-4)
[tex]-4=\frac{1}{3}(3)+b\\-4=1+b\\b=-4-1\\b=-5[/tex]
Putting the values of m and b
[tex]y=\frac{1}{3}x-5\\Multiplying\ whole\ equation\ by\ 3\\3y=x-5\\x-5=3y\\x-3y=5[/tex]
The linear equation passing through given points is: x-3y=5
Keywords: Linear equation, line equation
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