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What is an equation of the line that passes through the point (5,−2) and is parallel to the line 2x-5y=35?

User Ganesh Jadhav
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1 Answer

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Answer: 5y - 2x = -20 OR

y + 2 = ²/₅ (x - 5)

Explanation:

Find the slope of the given line

If we put the line 2x - 5y = 35 into the y = mx + c form, the coefficient of x (m) is the slope.

since 2x - 5y = 35

⇒ 5y = 2x - 35

y = ²/₅ x - 7

∴ the slope of the line is ²/₅

Identify the slope of the parallel line

When two lines are parallel, they have the same slope.

∴ the slope of the parallel is also ²/₅

Determine the equation of the parallel line

We can now use the point-slope form (y - y₁) = m(x - x₁)) to write the equation for this line where (x₁ , y₁) is (5,−2) :

y - (-2) = ²/₅ (x - 5)

y + 2 = ²/₅ (x - 5)

If we were to write the equation in the same form as the line that was given:

since y + 2 = ²/₅ (x - 5)

y = ²/₅ x - 2 - 2

y - ²/₅ x = - 4 [multiply through by 5]

5y - 2x = -20

To test my answer, I have included a Desmos Graph that I graphed using the information provided in the question and my answer.

What is an equation of the line that passes through the point (5,−2) and is parallel-example-1
User Cube Drone
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