Question

write an equation that is parallel to 3x-2y=14 and passes through point (-6,-11)

Answer 1

y = ($\frac{3}{2}$)x -2 is the equation of the required line

Step-by-step explanation:

Step 1 :

Equation of the given line is 3x-2y=14

Re writing this in the form y = mx + c , we have

-2y = -3x +14

 y = ($\frac{3}{2}$)x - 7

The co efficient of x , m is the slope of the line. So for the given line the slope is  $\frac{3}{2}$

Step 2 :

We have to find  equation of a line which is parallel to this line. All parallel lines will have the same slope. Hence the required line has a slope of $\frac{3}{2}$.

Step 3 :

Equation of line with slope m and passing through a point ($x_{1} ,y_{1}$) is

(y-$y_{1}$) = m((x-$x_{1}$)

So equation of line passing through (-6,-11) and with a slope of  $\frac{3}{2}$ is

(y-(-11)) = $\frac{3}{2}$ ( x - (-6))

y + 11 = $\frac{3}{2}$ ( x + 6)

y = ($\frac{3}{2}$)x + 9 - 11

y = ($\frac{3}{2}$)x -2

Step 4 :

Answer  :

y = ($\frac{3}{2}$)x -2 is the required equation