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marusya05 [52]
3 years ago
8

Write an equation In slope intercept form for the line that is parallel to the given line and that passes through the given poin

t
5x - 2y=10 (3 -5)
Mathematics
1 answer:
ludmilkaskok [199]3 years ago
5 0

The equation of the parallel line in slope-intercept form is;

y = \frac{5}{2} x - \frac{25}{2}

Step-by-step explanation:

Let us revise some facts about parallel lines

The equations of two parallel lines have:

  • Same slopes
  • Different y-intercept

The slope-intercept form of the equation of a line is y = m x + b, where m is the slope of the line and b is the y-intercept

The given line has equation 5x - 2y = 10

Put it in the form of y = m x + b to find its slope

∵ 5x - 2y = 10

- Subtract 5x from both sides

∴ -2y = 10 - 5x

- Divide to sides by -2

∴ y = -5 + \frac{5}{2} x

∴ y =  \frac{5}{2} x - 5

- The value of m is the coefficient of x

∴ m = \frac{5}{2}

∴ The slope of the given line is \frac{5}{2}

∵ Parallel lines have same slopes

∴ The slope of the parallel line is m = \frac{5}{2}

- Substitute the value of m in the form of the equation

∴ The equation of the parallel line is y = \frac{5}{2} x + b

To find b substitute x and y in the equation by the coordinates of any point lies on the line

∵ The parallel line passes through point (3 , -5)

- Substitute x and y by the coordinates of the point (3 , -5)

∵ x = 3 and y = -5

∴ -5 = \frac{5}{2} (3) + b

∴ -5 = \frac{15}{2} + b

- Subtract \frac{15}{2} from both sides

∴ b = \frac{-25}{2}

∴ The equation of the parallel line is y = \frac{5}{2} x + \frac{-25}{2}

∴ The equation of the parallel line is y = \frac{5}{2} x - \frac{25}{2}

The equation of the parallel line in slope-intercept form is;

y = \frac{5}{2} x - \frac{25}{2}

Learn more:

You can learn more about the equations of parallel lines in brainly.com/question/8628615

#LearnwithBrainly

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