What equation of the line passes through (4,7) and USB perpendicular to the graph of the life ne that passes through the points (2,3) and (-4,9)?

Question

Perpendicular lines

Answer 1

The slope of the line that passes thourgh (2,3) and (-4,9) is M=(9-3)/(-4-2) = 6/(-6) = -1

 

 Perpendicular lines have slopes that are NEGATIVE reciprocals of each other.

 

So the perpendicular line has slope M=1

 

It passes through (4,7) so x=4 when y = 7 and has slope 1

 

 y = M x + b

7 = 1*4 + b

7 = 4 + b

b  = 3

 

The perpendicular line equation is y = 1*x + 3 = x + 3

Answer 2

Hi Nat, perpendicular lines have slopes that are negative reciprocals of each other. The slope of a line between 2 points can be calculated by (Y₂ - Y₁) / (X₂ - X₁).

 

Use the information above:

 

1) The slope of the line that passes through (2,3) (-4,9) is (9-3) / (-4-2) = (6) / (-6) = -1

 

2) The slope of the line perpendicular to that line has a slope of 1 (because 1 is the negative reciprocal of -1)

 

3) The equation of the line we are looking for is y = mx + b where m = 1...so we have y = x + b

 

4) We can now plug in the point that (4,7) into  y = x + b......7 = 4 + b......b = 3

 

5) So the full equation of the line is y = x + 3