1. I'm given a slope of 1/4 and a set of 2 points each: p: (-12,6) & Q: (8,w) .find the value of w. what if the slope was -1/4, then what would the value of w be

2. What is the solution to these equations:
3x-2y-8=0
9x-6y-42=0
One solution, no solution or infinite solution or other?

Please help!!! Thanks:):):):)

since the slope is 1/4, you know that y will increase by 1 when x increases by 4.

Since x increased from -12 to 8 (20), y will increase by 1/4 (20) = 5. So, w=6+5=11.

If the slope had been -1/4, w = 6-5 = 1

#2. multiply the 1st equation by 3 and you now have

9x-6y-24=0
9x-6y-42=0

no solution there, eh? 9x-6y can't be both 24 and 42.

Thank u soooooooo MUCH!!!!!

1. To find the value of w given the slope and two points, you can use the point-slope formula:

y - y1 = m(x - x1)

where (x1, y1) are the coordinates of one point, m is the slope, and (x, y) are the coordinates of the unknown point.

For the first question, you are given the slope of 1/4 and the points P(-12,6) and Q(8,w). Let's substitute the values into the formula:

w - 6 = (1/4)(8 - (-12))

w - 6 = (1/4)(8 + 12)

w - 6 = (1/4)(20)

w - 6 = 5

To isolate w, add 6 to both sides of the equation:

w = 5 + 6

w = 11

So, the value of w is 11 when the slope is 1/4.

If the slope was -1/4, you would perform the same steps. Let's substitute the values into the formula:

w - 6 = (-1/4)(8 - (-12))

w - 6 = (-1/4)(8 + 12)

w - 6 = (-1/4)(20)

w - 6 = -5

To isolate w, add 6 to both sides of the equation:

w = -5 + 6

w = 1

So, the value of w would be 1 when the slope is -1/4.

2. To determine the solution to the system of equations, you can solve them using the method of elimination or substitution. Let's use the method of elimination:

Given equations:
3x - 2y - 8 = 0 (equation 1)
9x - 6y - 42 = 0 (equation 2)

Multiply equation 1 by 3 and equation 2 by -1 to create equal coefficients for x:

9x - 6y - 24 = 0 (equation 3)
-9x + 6y + 42 = 0 (equation 4)

Now, add equations 3 and 4:

(9x - 6y - 24) + (-9x + 6y + 42) = 0

The x-term cancels out, and the y-term cancels out as well. We're left with:

-24 + 42 = 0

18 = 0

Since 18 does not equal 0, we have a contradiction. This implies that the system of equations has no solution.

Therefore, the solution to the system of equations: 3x - 2y - 8 = 0 and 9x - 6y - 42 = 0 is no solution.