Question

determine the equation of the line through point (2.4) and parallel to the line 2y-3x + 7 = 0!

Answer 1

We first look for the gradient in the line equation 2y - 3x + 7 = 0

We form into a general form

y = mx + x

2y = 3x - 7

y = 3 / 2x - 7/2

So, it can be concluded that the m is 3/2. Because it's parallel, then m1 = m2.

We make a new equation that passes point (2, 4) -> [2 as x1 and 4 as y1].

y = m (x - x1) + y1

y = 3/2 (x - 2) + 4

y = 3 / 2x - 3 + 4

y = 3 / 2x + 1

2y = 3x + 2

2y - 3x - 2 = 0

So, the equation of the line through point (2.4) and parallel to line 2y - 3x + 7 = 0 is 2y - 3x - 2 = 0

Answer 2

Answer:

3x−2y+9=0.

Explanation:

Recall that the eqn. of a line parallel to the given line

l1:ax+by+c=0 is of the Form l2:ax+by+c'=0,c'≠c.

If we compare the slopes of the lines l1andl2, we will find that

the result is quite obvious. If, in addition, #(x_0,y_0) in l_2, then,

ax0+by0+c'=0, giving, c'=−ax0−by0.

∴l2:ax+by=ax0+by0.

Accordingly, the eqn. of the reqd. line is given by,

3x−2y=3(1)−2(6)⇒3x−2y+9