Question

A line passing through​ (6,a) and ​(9,−​4) is parallel to 2x−3y=6. What is the value of​ a?

Answer 1

Answer:

a= -17/2

Step-by-step explanation:

slope of line=3/2(parallel to given line so equal slope)

(a+4)/(6-9)=3/2

a+4= -9/2

a= -17/2

Answer 2

Given:

A ( 6 , a )   B ( 9 , - 4 )

Parallel to 2x − 3y = 6

To find :

The value of a.

Formula to be used:

Slope of two points = $\frac{y_{2} - y_{1} }{x_{2} - x_{1} }$

Slope of the equation , y = mx + c

Solution:

Step 1 of 3:

Slope of two points = $\frac{y_{2} - y_{1} }{x_{2} - x_{1} }$

Slope of two points = $\frac{-4-a}{9 - 6}$

Slope of two points, $m_{1}$ = $\frac{-4-a}{3}$

Step 2 of 3:

Slope of the equation ,  y = mx + c

From the given equation ,

3y = 2x - 6

Divided by 3 on both sides ,

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

slope of equation, $m_{2}$ = $\frac{2}{3}$

Step 3 of 3:

If the two lines are parallel to each other then their slopes are equal,

Therefore $m_{1} = m_{2}$

On substituting ,

$\frac{-4-a}{3} = \frac{2}{3}$

- 4 - a = 2

a = -4 - 2

a = - 6

Final answer:

The value of​ a is - 6.