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.