How do you find the equation of the line through point (-6, -1) perpendicular to line 5x − 3y = 2?
Straight lines are a very important concept related to mathematics and have immense applications in the field of geometry. The straight lines form the backbone of different polygons and polyhedrons. They can be represented in the cartesian plane by using linear equations. Let's solve a question related to straight lines.
Answer: The equation of the line through point (-6, -1) perpendicular to line 5x - 3y = 2 is 3x + 5y + 23 = 0.
Let's understand the solution in detail.
In this problem, to find the line perpendicular to another line, we use the formula m1 × m2 = -1.
We can re-write the equation as y = 5x/3 - 2/3
Hence, here, m1 = slope of line given = 5/3
Hence, by using the formula above, we find m2 = -3/5
Now, we use the point-slope form to find the required equation.
Hence, the equation is: y - (-1) = -3/5 (x - (-6)) (according to the given point)
⇒ 5 (y + 1) = -3 (x + 6)
⇒ 3x + 5y = -23
Hence, the equation of the line through point (-6, -1) perpendicular to line 5x - 3y = 2 is 3x + 5y + 23 = 0.