Question

Write equation parallel to 2x+5y=15 -10 1

Answer 1

The equation of the line parallel to 2x + 5y = 15 and passes through point (-10 , 1) is y = $\frac{-2}{5}$ x - 3

Step-by-step explanation:

Parallel lines have:

• Equal slopes
• Different y-intercept

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 = $\frac{-2}{5}$ x + 3

- find the value of m from the equation

∵ y = m x + b

∴ m = $\frac{-2}{5}$

∵ Parallel lines have same slopes

∴ The slope of the parallel line is $\frac{-2}{5}$

- Substitute it in the form of the equation

∵ y = m x + b

∵ m = $\frac{-2}{5}$

∴ y = $\frac{-2}{5}$ 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 = $\frac{-2}{5}$ (-10) + b

∴ 1 = 4 + b

- Subtract 4 from both sides

∴ -3 = b

∴ y = $\frac{-2}{5}$ x - 3

The equation of the line parallel to 2x + 5y = 15 and passes through point (-10 , 1) is y = $\frac{-2}{5}$ x - 3

Learn more:

You can learn more about the equations of parallel lines in brainly.com/question/9527422

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