<h2>Answer: 5y - 2x = -20 OR </h2><h2> y + 2 = <em>
²/₅</em> (x - 5)</h2>
<h3>Step-by-step explanation:</h3>
<u>Find the slope of the given line</u>
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
<em> ∴ the slope of the line is ²/₅</em>
<u>Identify the slope of the parallel line</u>
When two lines are parallel, they have the same slope.
∴ the slope of the parallel is also ²/₅
<u>Determine the equation of the parallel line</u>
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) = <em>²/₅</em> (x - 5)
y + 2 = <em>²/₅</em> (x - 5)
If we were to write the equation in the same form as the line that was given:
since y + 2 = <em>²/₅</em> (x - 5)
y = <em>²/₅</em> x - 2 - 2
y - <em>²/₅</em> x = - 4 [multiply through by 5]
5y - 2x = -20
<em>To test my answer, I have included a Desmos Graph that I graphed using the information provided in the question and my answer.</em>