The equation of line parallel to x+5y=2 passing through (6,8) is:
[tex]y=- \frac{1}{5}x+\frac{46}{5}[/tex]
Further explanation:
Given line is:
x+5y=2
We have to convert the given equation in point slope form
The point-slope form is:
y=mx+b
So
[tex]x+5y=2\\5y=-x+2\\\frac{5y}{5}=\frac{(-x+2)}{5}\\y=-\frac{1}{5}x+\frac{2}{5}[/tex]
The coefficient of x is the slope of the line.
m= -1/5
As the required line is parallel to given line then the slope of new line will be same.
[tex]y=mx+b\\Putting\ the\ value\ of\ m\\ y=- \frac{1}{5}x +b[/tex]
For finding the value b, put (6,8) in equation
[tex]8=- \frac{1}{5}(6) +b\\8=- \frac{6}{5}+b\\8+ \frac{6}{5}=b\\b = \frac{46}{5}[/tex]
Putting the values of b and m
[tex]y=- \frac{1}{5}x+\frac{46}{5}[/tex]
The equation of line parallel to x+5y=2 passing through (6,8) is:
[tex]y=- \frac{1}{5}x+\frac{46}{5}[/tex]
Keywords: Slope, Point-slope form
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