A)The equation of a line β is 2x-3y=6
find the gradient of β
b) find the equation of the line which is parallel to β and passes through the point (6,9)

a) 2/3

b)

Step-by-step explanation:

b) From my previous answer...

Since parallel lines have the same gradient,

the gradient of the line is 2/3 too.

Thus, m= 2/3.

y= 2/3x +c

Now substitute a coordinate into the equation to find c, the y-intercept.

When x=6, y=9,

9= (2/3)(6) +c

9= 4 +c

c= 9 -4

c= 5

Thus the equation of the line is y= 2/3x +5.

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