write an equation of the line that passes through the point (2,-3) and is perpendicular to the line -2x+5y=3

Question

write an equation of the line that passes through the point (2,-3) and is perpendicular to the line -2x+5y=3

Answer 1

-2x + 5y = 3

5y = 2x + 3

y = (2/5)x + 3/5      The slope of this line is 2/5. Since perpendicular lines have slopes that are negative reciprocals of each other, the new line will have a slope of -5/2. Now, you have a point (2,-3) and a slope; so, you can use the point-slope form of the equation of a line.

y - y₁ = m(x - x₁)

y + 3 = -5/2(x - 2)

y +3 = (-5/2)x + 5

y = (-5/2)x + 2