A line through point (-3,4) is perpendicular to the line y = 2x - 3. Find the point where the lines intersect?

Answer 1

Given that we have a point for which a line must go through and is perpendicular, we can determine the slope of the perpendicular line...

Perpendicular lines has the product of there slopes = -1

Line #1 --> y₁ = 2x - 3 SLOPE = 2

Line #2 --> y₂ = mx + b SLOPE = -1/2

Therefore: Line #2 --:> y₂ = -x/2 + b

Now we fit this line to go through the point in question...

4 = -1/2 * (-3) + b

b = 5/2

Line #2 --> y₂ = ( 5 - x )/2

This line is perpendicular to the given line and goes through the point requested. Now we look to see where they intersect by setting the equations equal...

y₁ = y₂ --> 2x - 3 = ( 5 - x )/2

2x + x/2 = 3 + 5/2

( 5/2 ) x = 11/2

x = (11/2)/(5/2) --> 11/5

Therefore the point in intersection is...

(11/5, 7/5) --> just plug in the value of x found in the previous line into either of the two equations you have