(x1, y1) = (0,4) so the y intercept is b = 4

(x2, y2) = (6,0)

gradient formula

m = (y2-y1)/(x2-x1) = -4/6 = -2/3

so

y = mx + b

gives

y = (-2/3)x + 4

* Find the equation of the line which passes through (0,2) and is parallel to AB.

parallel means it has the same gradient m = -2/3

so the equation is of the form

y = (-2/3)x + c

substitute (x,y) = (0,2) gives

c = 2 as the y intercept

so

y = (-2/3)x + 2

* Find the equation of the line which passes through the midpoint of AB and is perpendicular to AB.

the midpoint formula averages the x & y values respectively

(xm,ym) = ( (x1+x2)/2 , (y1+y2)/2 ) = (3,2)

and

since it is perpendicular it has gradient n = -1/m = 3/2

so the equation is of the form

y = nx + d = (3/2)x + d

substitute (x,y) = (3,2) gives

2 = (3/2)3 + d

so d = -4/9 is the y intercept

then

y = (3/2)x – (4/9)

.

A-B : as a straight line it will have an equation Y=mX + C

now C will be the value of Y when X=O, in this case 4.

m is the gradient ( negative in this case ) ie how much does Y change per unit X, in this case -4 / 6. Assembled and cancelled out – this makes an equation Y = -2X/3 + 4.

Checkout : when X=0, Y= 4 ok…When X=6, Y=0 also ok. All I have time for now………………