The line on the graph passes through the points A (1, 3) and B (7, 1). YA
a) Calculate the gradient of line AB.
b) Find the gradient of a line perpendicular
to AB.
+
A
D
c) Find the equation of the line passing
through point (4, 2) and perpendicular
to AB.

Step-by-step explanation:

a) gradient of AB

  or

  Slope of AB

b)

when lines are perpendicular to each other, the product of their slope = - 1

That is ,

c) Equation of the line perpendicular to line AB and passing through ( 4 , 2 )

x=-2

infinite number of lines, so there is an infinite number of equations.

step-by-step explanation:

there are an infinite number of line that passes through the point (-2,5)

x=-2   is one line that passes through the point

y = 5 is another line that passes through the point

(these two lines are perpendicular to each other).

since the number of   numbers are infinite and the slope is the ratio of two numbers,(change in y over change in x) we can have an infinite number of slopes.     our only condition is that it passes through the point (-2,5)