please help with these problems.......?

Question

here are some questions i really need answers, 1.how could you change the ptich of a roof to make it steeper? Use rise and run in your explination. 2.whats the slope of y=1/3x+2,3. write an equation for the line that passes thorugh the points (2,7) and (-4,4) please answer any you can, and say which one it is.

Answer 1

1. Steeper lines have higher slopes. This means the rise is greater in relation to the run. A roof that has a 45 degree slope (which is quite steep for a roof) has a slope of 1. Anything steeper has a slope greater than 1. Anything less steep has a slope less than 1. A flat roof has a slope of zero.

2. The slope of the given line is 1/3. I know this because the equation is in slope intercept form, y = mx + b, where m is the slope and b is where the line crosses the y axis

3. First, find the slope:

(7 - 4)/(2 - -4) = 3/6 = 1/2

Then, plug the slope and one of the ordered pairs into the slope intercept formula to find the y-intercept, called "b":

7 = (1/2)(2) + b
7 = 1 + b
6 = b

then plug the slope and the y intercept into the slope/y-intercept formula:

y = (1/2)x + 6

Answer 2

I see you're exploring graphs.
To change the pitch of a roof, you must first understand the term "pitch" in reference to roofing. The term simply refers to the slope of the roof - or how much higher (rise) it becomes as you move (run) toward the center. That being said, to make the roof steeper, you must make it higher. Imagine pinching the highest point in the roof and stretching it upward. Now think of what you have just done. You've made the top higher (rise) and the length from the edge to the top (run) shorter.

The equation you've been given (y=1/3x+2/3) is in point-slope form. That being said, you know you're given two key points of information. 1) A point. 2) A slope. The general form of point-slope is y=mx+b, where m is equal to the slope (rise/run) and b is equal to a y-intercept (where the line meets your Y-axis).

For an equation through your points, you need to know the point-slope equation for a line [(y-y1)=m(x-x1)]. Obviously, this includes two details. 1) A point. 2) A slope. You're already given a point - two, in fact! To find the slope (rise/run) given two points, you need to know the formula for doing so. (y2-y1/x2-x1).
Remember, slope is only the rise over the run. Imagine a point moving along the Y-Axis, and only the Y-Axis. This point can only move up and down. This would be your rise. Remember, Y-Axis = Rise. Now imagine the same for a point on your X-Axis. This point only moves side to side, never up or down. This would be your run. Remember, X-Axis = Run.
That being said, (y2-y1/x2-x1) = (rise/run). The two Y variables are given to you. Remember, plots are given to you in the form (x,y). The first point (2,7) would be put into the equation like (y2-7/x2-2). The second point (-4,4) would make it (4-7/-4-2). Now all you have to do to find the slope is solve. 4-7=-3. -4-2=-6. You're left with (-3/-6). Remember, two negatives make a positive. So think of it simply as 3/6, and reduce it to 1/2. Your slope for a line between points (2,7) and (-4,4) is 1/2.
Let's go back to the point-slope equation [(y-y1)=m(x-x1)]. Recall that the m stands for the slope, which we have now found. We're left with (y-y1)=1/2(x-x1). Now fill in the point. Either point will work. Let's try (2,7). You get (y-7)=1/2(x-2) when you fill in the point. Next, distribute your 1/2 through (x-2). You have to multiply everything in (x-2) by 1/2, and after doing so you're left with (1/2x-1).
Your formula now looks like (y-7)=1/2x-1. You're almost there! All that's left is to move that pesky 7 to get it into a slope-intercept form. (y=mx+b). All you have to do, since it's y-7, is add a 7 to both sides. This cancels the 7 on the left, and adds 7 to the -1 on the right.
Your final answer is y=1/2x+6.

Thanks.
=)

Answer 3

1. not sure...

2. 1/3 is the slope

3. (2,7) and (-4,4)
first step is to find the slope (4-7)/(-4-2) so slope or m = 1/2

plug one of the points and the slope into y-y1 = m(x-x1)
we get y-7=1/2(x-2)
y-7 = (1/2)x - 1
y= (1/2)x +6 <---this is the equation

Answer 4

1- not sure!!

2- y=mx+b ... comparing, we have slope=m=1/3

3- using the two-point form ( y-y1 )/ (y2-y1) = (x-x1) / (x2-x1)
s'pose (2,7) = (x1,y1) and (-4,4) = (x2,y2)
using the formula above,

y - 7 x-2
____ = ______
4 - 7 -4 - 2

cross multiplying:

=> (-4 - 2) * (y - 7) = (4 - 7) * (x - 2)

=> (-6) (y - 7) = (-3) (x - 2)

=> -6y + 42 = -3x + 6

Thus, the eqn is

-6y + 3x + 42 - 6 = 0

=> 3x - 6y + 36 = 0

=> 3 ( x - 2y + 12) = 0

+-----------------------+
| x - 2y + 12 = 0 |
+-----------------------+

Answer 5

what is the slope of y=1/3x + 2
that follows the slope intercept form y=mx+ b, where m is the slope so the slope in your equation is 1/3

Answer 6

2. y0ur slope is 1/3!

(given equation in y=mx+b, whatever the coefficient of your x is your slope.

3. given that, you first need to find the sl0pe.

m(sl0pe)=change in y / change in x

m= (4-7)/(-4-2)

m= -3/-6 or 1/3

then use this formula
y-ysub1 = m(x-xsub1)

y+7=1/3(x-4)

3y+21=x-4

x-3y-25 = 0 (final answer)

Answer 7

%100 sure for the equation of (2,7) and (-4,4)
y=1/2x+6