Question

1.) Write 6x-3y=3 in slope form.
Show all work!

2.) Based on your answer to the question above, state the slope and the y-intercept of the line.

3.) Based on the two previous questions. Find the line that is perpendicular to this line and passes through (4,-2).

Answer 1

1. 6x - 3y = 3 (subtract 6x from both sides)
-3y = -6x + 3 (divide by -3)
y = -6/-3x + 3/-3
y = 2x - 1 <== slope intercept form

2. In y = mx + b form, the slope is in the m position and the y intercept is in the b position. Therefore, the slope of this line is 2 and the y intercept is -1.

3. If you are looking for a perpendicular line, you need the negative reciprocal of the slope given. All that means is " flip " the slope and change the sign. The slope given is 2 or 2/1, the negative reciprocal slope you need is -1/2 (see how I flipped the slope and changed the sign...
Now we will use y = mx + b and solve for b because we already know that the slope is -1/2.
y = mx + b
slope(m) = -1/2
(4,-2) x = 4 and y = -2
now we sub
y = mx + b
-2 = -1/2(4) + b
-2 = - 2 + b
-2 + 2 = b
0 = b
your perpendicular line is : y = -1/2x + 0

Answer 2

Thank you.

Answer 3

no problem :)