The equation of the line parallel to 2x + 5y = 15 and passes through point (-10 , 1) is y = [tex]\frac{-2}{5}[/tex] x - 3
Step-by-step explanation:
Parallel lines have:
We need to write the equation of a line that paralegal to the line
2x + 5y = 15 and passes through point (-10 , 1)
Put the equation of the given line in the form of y = m x + b, where m is the slope of the line and b is the y-intercept
∵ 2x + 5y = 15
- Subtract 2x from both sides
∴ 5y = -2x + 15
- Divide both sides by 5
∴ y = [tex]\frac{-2}{5}[/tex] x + 3
- find the value of m from the equation
∵ y = m x + b
∴ m = [tex]\frac{-2}{5}[/tex]
∵ Parallel lines have same slopes
∴ The slope of the parallel line is [tex]\frac{-2}{5}[/tex]
- Substitute it in the form of the equation
∵ y = m x + b
∵ m = [tex]\frac{-2}{5}[/tex]
∴ y = [tex]\frac{-2}{5}[/tex] x + b
- To find the value of b substitute x and y in the equation by the
coordinates of any points on the line
∵ The parallel line passes through point (-10 , 1)
∴ x = -10 and y = 1
∵ 1 = [tex]\frac{-2}{5}[/tex] (-10) + b
∴ 1 = 4 + b
- Subtract 4 from both sides
∴ -3 = b
∴ y = [tex]\frac{-2}{5}[/tex] x - 3
The equation of the line parallel to 2x + 5y = 15 and passes through point (-10 , 1) is y = [tex]\frac{-2}{5}[/tex] x - 3
Learn more:
You can learn more about the equations of parallel lines in brainly.com/question/9527422
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