Question

A line whose equation is 3/2y =3x-6 is parallel to a line with a general equation ax+by+c=0 passing through the points (3,2) . Find the value of a,b and c.​

Answer 1

Answer:

$\frac{1}{6} x+3y+\frac{13}{2}$    or    x + 18y + 39

Step-by-step explanation:

$\frac{3}{2} y$ = $3x-6$

→ First multiply everything by 2 to get rid of the fraction

3y = 6x - 12

→ We want to find the equation that's parallel to this line and passes through (3 , 2). The first thing we know about parallel lines is that the gradient is the negative reciprocal so,

$3y = -\frac{1}{6} x+c$

→ Now we substitute in the values (3 , 2)

$6 =- \frac{1}{2}+c$

→ Add  $\frac{1}{2}$  to both sides to isolate c

$\frac{13}{2} =c$

So the equation of the line that is parallel to  $\frac{3}{2} y$ = $3x-6$  is  $3y =- \frac{1}{6} x+\frac{13}{2}$      but we are not finished we are asked to but the equation in the format

ax + by + c = 0  so,

$3y =- \frac{1}{6} x+\frac{13}{2}$

Rearrange

$\frac{1}{6} x+3y+\frac{13}{2}$

If the question want's the answer in whole numbers then multiply everything by 6

x + 18y + 39