Question

Find the distance between the lines with the given equations. 3x+y = 1 y+6=-3x

Answer 1

Answer:

• 2.21 units

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Given lines:

• 3x + y = 1 and  y + 6 = - 3x

Convert both equations to slope-intercept form of y = mx + b:

• 3x + y = 1 ⇒ y = - 3x + 1
• y + 6 = - 3x ⇒ y = - 3x - 6

Slopes are same, so these are parallel lines, and the distance between parallel lines is:

• $d=\cfrac{|b_1-b_2|}{\sqrt{1+m^2} }$, where b₁, b₂ - y-intercepts, m- slope

Substitute and calculate:

• $d=\cfrac{|1+6|}{\sqrt{1+(-3)^2} }=\cfrac{7}{\sqrt{10} } =2.21$