Write the equation of the line perpendicular to -6x+3y=6 that passes through (2,0). write you answer in slope-intercept form

i have down
y = mx + b
-6x+3y=6
3y= -6x +6
y = -2x + 2
so far

The answer is: y - 0 = -1/2(x - 2)

Step-by-step explanation:

Given - an equation in standard form:

-6x + 3y = 6

Solve for y:

Add 6x to both sides:

3y = 6 + 6x

y = 2 + 2x

y = 2x + 2, so the slope is 2.

The perpendicular slope is the negative inverse of 2, which is -1/2.

Point slope form is:

y - y1 = m(x - x1)

Substitute in the numbers from the point (2,0) and the slope -1/2:

y - 0 = -1/2(x - 2)

Taking it to y intercept form:

y = -1/2x + 1

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

Step-by-step explanation:

Thank you for sharing the work you've already done!  If we solve -6x+3y=6 for 3y, by adding 6x to both sides, we get 3y = 6x + 6, or (solving for y)

y = 2x + 2.  Compare this to your work.

If this given line -6x+3y=6 has the slope m = 2, then any line perpendicular to it has the slope -1/2, the negative reciprocal of 2.

Now, knowing this new slope and the fact that (2, 0) lines on a line perpendicular to -6x+3y=6, we use the slope-intercept formula, with m = -1/2, y = 0 and x = 2:

That formula, y = mx + b, becomes 0 = -1/2 + b.  Thus, b = 1/2, and the desired equation is

y = (-1/2)x + 1/2.

center (1,3) with radius 6

step-by-step explanation:

we must complete the square to find the center and radius of the circle.

first make sure the x and y squared terms have 1 as their coefficients. we also make sure x and y terms together.

we now create space between the x and y terms with parenthesis.

we complete the square by taking the middle terms -2x and the -6y - divide each and square them.

we add the squares to both sides.

simplify.

and write the quadratics in factored form.

the center is (h,k) or (1,3). the radius is the square root of 36 which is 6.