Answer: 5y - 2x = -20 OR
y + 2 = ²/₅ (x - 5)
Step-by-step 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.
