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

$y = \frac{8}{7} x + 3$

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,

$y = \frac{9}{2} x + 3.$

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,

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

$- 5 - 3 = - 7m$

$- 7m = - 8$

$m = \frac{8}{7}$

The required equation is

$y = \frac{8}{7} x + 3$

Or

$7y = 8x + 21$

$7y-8x =21$

Answer 2

Answer: 8x - 7y = -21

Step-by-step 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,

$y-3= \frac{-5-3}{-7-0} (x-0)$

$y-3= \frac{-8}{-7} (x)$

-7y+21=-8x

8x - 7y + 21=0

⇒ 8x - 7y = -21

Which is the required equation of the line.