Respuesta :

mariazahra22

Step-by-step explanation:

When lines are perpendicular to each other

multiplying their gradients(m) will equal to - 1

so , m1 × m2 = -1

1st:Find m1

5x+6y= -6

make y the subject,

6y= -5x -6

[tex]y = \frac{ - 5x - 6}{6} [/tex]

y= -5/6x - 1

because y = mx + c

m1 = -5/6

2nd:find m2

-5/6 × m2 = -1

m2 = 6/5

3rd: substitute m2 and the coordinates into y=mx+c

y=mx+c

-1= (6/5)(-2)+c

-1 = -12/5 + c

-5 = -12 + c

-5+12= c

c = 7

4th: substitute m2 and c into y= mx+c to find the equation the line

y =6/5x + 7 (Ans)

As per slope-intercept form, the equation of the line through point (−2,−1) and perpendicular to 5x + 6y = -6 is 5y = 6x + 7.

What is the slope-intercept form of a straight line?

The slope-intercept form of a straight line is y = mx + c.

Here, 'm' is the slope and 'c' ix the y-intercept of the given line.

The given equation is 5x + 6y = - 6

Therefore, in slope-intercept form, this equation will be:

y = - 5x/6 - 1

Therefore, the slope of this line is m = - 5/6 and the y-intercept is c = - 1.

The required line is perpendicular to the given line.

Therefore, the slope of the required line is

= - 1/m

= 6/5

Again, the required line passes through the point (- 2, - 1).

Therefore, - 1 = - 2(6/5) + c

⇒ c = - 1 + 12/5

⇒ c = 7/5

The equation of the required line is

y = (6/5)x + 7/5

⇒ 5y = 6x + 7

Learn more  about the slope-intercept form of a straight line here: https://brainly.com/question/14534555

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