Write the equation of the line that passes through the given point and is perpendicular to the given line. (0, 3); 3x − 4y = −8

  y = -4/3x + 3

Step-by-step explanation:

3x − 4y = −8

-4y = -3x - 8

y = 3/4x + 2

slope m = 3/4

perpendicular version of it is opposite inverse: -4/3

y-intercept through point (0, 3):

y = mx + b

3 = -4/3(0) + b

b = 3

Use the perpendicular slope with b from above to form new perpendicular equation of line:

y = mx + b

y = -4/3x + 3

simplifying

5(x + -6) = 2(x + 3)

reorder the terms:

5(-6 + x) = 2(x + 3)

(-6 * 5 + x * 5) = 2(x + 3)

(-30 + 5x) = 2(x + 3)

reorder the terms:

-30 + 5x = 2(3 + x)

-30 + 5x = (3 * 2 + x * 2)

-30 + 5x = (6 + 2x)

solving

-30 + 5x = 6 + 2x

solving for variable 'x'.

move all terms containing x to the left, all other terms to the right.

add '-2x' to each side of the equation.

-30 + 5x + -2x = 6 + 2x + -2x

combine like terms: 5x + -2x = 3x

-30 + 3x = 6 + 2x + -2x

combine like terms: 2x + -2x = 0

-30 + 3x = 6 + 0

-30 + 3x = 6

add '30' to each side of the equation.

-30 + 30 + 3x = 6 + 30

combine like terms: -30 + 30 = 0

0 + 3x = 6 + 30

3x = 6 + 30

combine like terms: 6 + 30 = 36

3x = 36

divide each side by '3'.

x = 12

simplifying

x = 12

this should .

i would say true? if the unit was informational and it "refreshed your understanding", then true.