Answer:
A) The gradient of
is
B) Point M is (2,2.5)
C) The gradient of
is
y =
x +
Explanation:
A)
The gradient is the slope. What is the
(the change in y over the change in x)
From the two points given, if I start at point A and go to point B, I am going down 5 and then to the right 4, my y is decreasing by 5 while my x is increasing by 4, so the slope is:
B)
We have two points (0,5) and (4,0) We want to find the middle of those two points. Ordered pairs are in the form (x,y) We will find the average of our x's and the average of our y's
x =
= 2
y =
2.5
So the ordered pair in the middle is (2,2.5)
C)
Perpendicular lines have opposite inverse slopes. Since
's slope was
, the line that is perpendicular to it would be
To write the equation we will need the slope, and x(2) and a y(2,5) We are getting the (x,y) from point M (2,2.5)
y = mx + c
2.5 =
(2) + c We are solving for C
2.5 =
+ c Subtract
from both sides. I will convert 2.5 to
-
=
-
+ c
-
= c
= c
y =
x +