Question

Write an equation in standard form for the line passing through (-7,-5) and having the day y-intercept as 9x-2y=-6

Answer 1

ANSWER


`y = (8)/(7) x + 3`

or


`7y-8x =21`

EXPLAIN

Let the equation of the line be


`y = mx + b`

Where

`b`
is the y-intercept and

`m`
is the slope.

We can determine the y-intercept from the equation given to us.


`9x - 2y = - 6`

We rewrite this line in the slope intercept form to get,


`- 2y = - 9x - 6`

Thus implies,


`y = (9)/(2) x + 3.`

The y-intercept is

`3.`
Since the equation we are finding also has the same y-intercept,

`b = 3.`

We substitute this value into our equation to get,


`y =mx + 3`

The equation passes through

`(-7,-5)`
It must therefore satisfy its equation.

This implies that,


`-5 = m( - 7) + 3`


`- 5 - 3 = - 7m`


`- 7m = - 8`


`m = (8)/(7)`

The required equation is


`y = (8)/(7) x + 3`

Or


`7y = 8x + 21`


`7y-8x =21`

Answer 2

Answer: 8x - 7y = -21

Explanation:

Since, the line has the y-intercept same as 9x-2y=-6

And for the y-intercept of the line x =0

⇒ y = 3

Therefore, y-intercept of the line 9x-2y=-6 is (0,3)

Thus, the line passes through the points ( -7,-5) and (0,3)

Therefore equation of the line,

`y-3= (-5-3)/(-7-0) (x-0)`

`y-3= (-8)/(-7) (x)`

-7y+21=-8x

8x - 7y + 21=0

⇒ 8x - 7y = -21

Which is the required equation of the line.