Will mark ! : )a.) what is the equation of a line that is parallel to −x+3y=6 and passes through the point (3, 5)? b.) what is the equation of a line that is perpendicular to 2x+y=−4 and passes through the point (2, −8)?

A) y = 1/3x + 4

B) y = 1/2x - 9

Step-by-step explanation:

A) In order to find this, we must first solve the initial equation for y to get the slope.

-x + 3y = 6

3y = x + 6

y = 1/3x + 2

Now we know the slope to be 1/3 since parallel lines have the same slope. So we take this slope and the point and use point-slope form to find the equation.

y - y1 = m(x - x1)

y - 5 = 1/3(x - 3)

y - 5 = 1/3x - 1

y = 1/3x + 4

B) To find this line, we again have to find the slope of the initial equation by solving for y.

2x + y = -4

y = -2x - 4

Now we know our new slope to be 1/2. This is because perpendicular lines have opposite and reciprocal slopes. We can use this and the point to solve in the same way.

y - y1 = m(x - x1)

y - - 8 = 1/2(x - 2)

y + 8 = 1/2x - 1

y = 1/2x - 9

center= (-2,0)

radius= sqrt2/2

step-by-step explanation:

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 .