Question

15. A line is parallel to the line x + 3y = 9 and passes through the point A (2, 7). Find its
equation​

Answer 1

So the line, say 'l', has the same slope as that of the line x + 3y = 9, since both are parallel.

x + 3y = 9

3y = - x + 9

y = - (x / 3) + 3

Now we get the equation in slope - intercept form, y = mx + c. So we get,

m = - 1 / 3

So slope of the line l is - 1 / 3.

Given that this line passes through A(2, 7). So we can have the point, slope form,

y - y1 = m(x - x1)

So,

y - 7 = - (x - 2) / 3

3y - 21 = 2 - x

x + 3y = 23

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Short cut...

We know that the equation of a line is given by,

y = mx + c.

From this,

x - y/m = - c/m

Since 'l' has same slope as that of the given line, 'm' in the equation of line 'l' should be same with the given one, but the y intercept 'c' differs.

So the LHS remains same as that of x + 3y = 9 but RHS varies. Let the equation of 'l' be,

x + 3y = k.

We have the point A(2, 7). Taking x = 2 and y = 7 in the equation,

2 + 3 × 7 = 23.

Hence we got the equation:

x + 3y = 23

One advantage of this method is that we don't have to find out the value of any other parameter additionally, like 'm'.

Answer 2

Answer:

A line is parallel to the line x + 3y = 9 and passes through the point

A(2,7). Find its equation