Respuesta :

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,

[tex]y-3= \frac{-5-3}{-7-0} (x-0)[/tex]

[tex]y-3= \frac{-8}{-7} (x)[/tex]

-7y+21=-8x

8x - 7y + 21=0

⇒ 8x - 7y = -21

Which is the required equation of the line.

kudzordzifrancis
ANSWER

[tex]y = \frac{8}{7} x + 3[/tex]

or

[tex]7y-8x =21[/tex]

EXPLAIN

Let the equation of the line be

[tex]y = mx + b[/tex]

Where
[tex]b[/tex]
is the y-intercept and
[tex]m[/tex]
is the slope.

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

[tex]9x - 2y = - 6[/tex]

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

[tex] - 2y = - 9x - 6[/tex]

Thus implies,

[tex]y = \frac{9}{2} x + 3.[/tex]

The y-intercept is
[tex]3.[/tex]
Since the equation we are finding also has the same y-intercept,
[tex]b = 3.[/tex]

We substitute this value into our equation to get,

[tex]y =mx + 3[/tex]

The equation passes through
[tex](-7,-5)[/tex]
It must therefore satisfy its equation.

This implies that,

[tex] -5 = m( - 7) + 3[/tex]

[tex] - 5 - 3 = - 7m[/tex]

[tex] - 7m = - 8[/tex]

[tex]m = \frac{8}{7} [/tex]

The required equation is

[tex]y = \frac{8}{7} x + 3[/tex]

Or

[tex]7y = 8x + 21[/tex]

[tex]7y-8x =21[/tex]

Otras preguntas