is anyone good with algebra one and two?? pleeeeease help!!?

Question

I need help with slopes and things of that nature.
For example: write an equation in slope-intercept form containing (9,-3) and (0,5) or passing through (3,4) and (5,8).

also.. I REALLY need help with word problems too, such as: a ski has a vertical drop of 1500 ft. over a distance of 4200 ft. what is the slope of the ski hill?

if u can help, please do so, thanx!

Answer 1

Remember, the slope of a line is defined as the change of the the y values, the vertical change, divided by the change in the x values, the horizontal change. So slope is defined this way:

m (slope) = (y - y') / (x - x').

Be careful when calculating the slope. Remember, when you plug coordinates of a point in to calculate the slope, always make sure you put them in the right order. For example, in your problem, if you let y = -3, then make sure you put its corresponding x coordinate, 9, in the same position in the denominator of the equation. Otherwise, all sorts of strange results occur. So, the above equation would look like this:

m = (-3 - y') / (9 - x') before putting in the coordinates of the other point, (0,5).

The final form of your equation for the slope will look like this:

m = (-3 -5) / (9 - 0) = -8 / 9.

So, your line has a negative slope, which means it drops down as you follow it from left to right.

The slope-intercept form for the equation of a line is y = mx + b. You have already calculated m. Now you need to find out the value for b. To do that, simply plug in the coordinates of any of your points which lie on the line into this equation. Make sure you put y and x values in their proper places. Using the point (9,-3), we get this:

-3 = (-8 / 9)(9) + b ----> -3 = -8 + b ---> -3 + 8 = 5 = b.

Your final slope-intercept equation here is:

y = (-8 / 9) x + 5.

For the last scenario, the vertical drop represents the change in y values, so (y - y') = 1500. The distance 4200 ft. represents the change in x values, so (x - x') = 4200. The slope in that case is:

1500 / 4200 = 15 / 42 = 5 / 14.

Notice that it says it has a vertical drop. That implies the slope is negative. So, we interpret the above slope as -5 / 14.

Answer 2

The formula for the slope of a straight line is y=mx + b. X and Y are variables. M and B are constants. Note that the direction of slope depends on the sign (positive or negative) of M. Also, B is the value of y when x = 0. Therefore, b will tell you where the line intersects the Y axis when x = 0. Now if we want the equation of a line that passes through (9,-3) and (0,5) then we find M and B and we are done. So total run = 9-0= 9. The rise = 5-(-3) = 8. Slope is rise/run =8/9 = 0.89 and is negative as it slopes down from left to right. So y=(-0.89)x + b. But we know that when y=0 then x=5, so B = 5. The equation of the line is y=(-0.89) x +5.

So suppose you have a equation y= 9x -3. Now if y = 0 then x = 1/3. If x = 0 then y = -3. So you now have two points to plot, (0,1/3) and (-3,0)Draw a line through them and you will see that the slope of the line (rise/run = slope) is 9.

your second question is easy, just remember that slope is rise devide by run (also know as the tangent of an angle). So Rise = 1.500 feet and the Run = 4,200. The slope is 1500/4200 or 0.3571. The inverse tangent of this number will give you the angle, so, arctan(0.3571) = 19.65 degrees.

Answer 3

To figure out the first one you have to put it in point-slope form which is:
y-y<1=m(x-x<1)
m is the slope which you also have to find
y-4=m(x-3)
the slope is
8-4
------- = = 2
5-3
so...
y-4=2(x-3)
y-4=2x-6
add 4 to both sides
y=2x-2..... and you have an equation in slope intercept form passing through(3,4) and (5,8)


and slope is rise over run
-1500/4200=-5/14

Answer 4

1.
slope intercept from: y=mx+b
for containing (9,-3) and (0,5):
m = slope = (y1-y2)/(x1-x2) = (5 - -3)/(0-9) = -8/9
y = -(8/9)x + b
put in a point:
5 = -(8/9)0 + b
5 = 0 + b
b = 5
y = -(8/9)x + 5

for passing through (3,4) and (5,8)
m = slope = (y1-y2)/(x1-x2) = (8-4)/(5-3) = 4/2 = 2
y = 2x + b
put in a point:
4 = 2(3) + b
4 = 6 + b
-2 = b
y = 2x - 2


2.
slope = y direction / x direction = rise/run = -1500/4200 = - 5/14

Answer 5

1)(9,-3) and (0,5)
Slope formula:
m=(y2-y1)/(x2-x1)
m=(5+3)/(0-9)
m=-8/9

Point-slope formula:
y-y1=m(x-x1)
y+3=-8/9(x-9)
y+3=-8/9x+8
y=-8/9x+5

2)(3,4) and (5,8)
m=(8-4)/(5-3)
m=4/2=2

y-4=2(x-3)
y-4=2x-6
y=2x-2

3)-1,500/4,200=
-5/14
You just divide the numerator and denominator by 300 to get the answer.

Answer 6

The formula is y=mx+b