Respuesta :

hafsakhanx

Answer: [tex]y = \frac{3}{4} x +1[/tex]

Step-by-step explanation:

A perpendicular line has slopes that are the opposite reciprocals of each other.

Step 1: Turn the given equation into slope-intercept form.

Given: 4x + 3y = 6 → Slope-Intercept Form: y = mx + b

                                         [tex]4x + 3y = 6[/tex]

                                          [tex]-4x[/tex]        [tex]-4x[/tex]

                                           [tex]\frac{3}{3}[/tex][tex]y[/tex] = [tex]\frac{4}{3} x[/tex] + [tex]\frac{6}{3}[/tex]

                                          [tex]y =[/tex] [tex]-\frac{4}{3}x + 2[/tex]

Step 2: Find the opposite reciprocal of the given slope.

                                           [tex]-\frac{4}{3}[/tex] → [tex]\frac{3}{4}[/tex]

Step 3: Take the slope of the new line and the given point and solve for "b" or y-intercept.

y = mx + b → (-8, -5)

-5 = [tex]\frac{3}{4}[/tex] (-8) + b

-5 = -6 + b

+6   +6

1 = b

Step 4: Take the slope and the value for b and plug them into the slope-intercept equation.

[tex]y = \frac{3}{4} x +1[/tex]

Polyblock

Answer:

y = 3x/4 - 1

Step-by-step explanation:

First, we need to find the slope of the given equation 4x + 3y = 6

Subtract 4x from both sides

4x + 3y = 6

- 4x        - 4x

3y = -4x + 6

Divide both sides by 3

3y/3 = (-4x + 6)/3

y = -4x/3 + 2

The slope of the given equation is -4/3

The slope of the perpindicular equation will have to be 3/4

Using slope intercept formula, we now have this

y = 3x/4 + b

Now plug in the given coordinate

-5 = 3(-8)/4 + b

-5 = -24/4 + b

-5 = -6 + b

Add 6 from both sides

-5 = -6 + b

+ 6  + 6

b = -1

Now we have y = 3x/4 - 1