I do not understand SLOPE!!!?

Question

I am having a very difficult time in my Algebra class learning how to calculate slope. My teacher rushes through the lecture, and leaves over half of the class in a stuper. Could someone, ANYONE, make an attempt to help me figure these problems out? And do you have any tips/suggestions that may make learning how to calculate slope any easier?

THANK YOU from the bottom of my heart to all who may answer and help me with this question!!!

Write an equation for each line passing through the given pair of points. Give the final answer in slope-intercept form.

1. (-1, -7) and (-8, -2)
2. (1/2, 3/2) and (-1/4, 5/4)

Write an equation of the line satisfying the given conditions. Give the final answer in slope-intercept form.

3. Parallel to 5x=2y+10; y intercept (0, 4)

Thanks again!!!

Answer 1

Slope is rise over run. Find the ratio of the difference of verticales (rise) to horizontals (run).

1. (x1, y1) (x2, y2) m=(y2-y1)/(x2-x1)

Using your numbers for 1 that gives us:

(-2 - -7)/(-8 - -1) = 5/-7 = -5/7

2. (5/4 - 3/2)/(-1/4 - 1/2) = (5/4 - 6/4)/(-1/4 - 2/4)

= (-1/4)/(-3/4) = 1/3

3. I don't like standard form, because the slope intercept form (y=mx+b) is beautiful, baby. So switch it around:

5x - 10 = 2y

y = 5/2x - 5

When the y intercept is (0,4), all you have to do is change b in the equation above (the y-intercept) to 4.

y = 5/2x + 4.

The lines are parallel because they each have the same slope.

Answer 2

The slope intercept form is y =mx + b where m is the slope and b is the y-intercept (which is where the line crosses the y-axis.

Slope is found by dividing the change iny by the chane in x.
So slope = (-2 -(-8))/(-8 -(-1)) = 6/-7= -6/7

So y = -6/7 +b
Find b by substituting the values of xand y from one ot the two given points. Doesn't matter which one.
-7 = -6/7 (-1) + b so b = -7-6/7 = -7 6/7
The final equation is y = -6x/7 - 7 6/7

Problem 2 will be done exactly the same as problem 1
Find slope - m = (5/4-3/2)/(-1/4-1/2)

Problem 3
5x +2y =10
2y = -5x +10
y = -5x/2 +5
This line has a slope of -5/2

So the slope of a line || to it must also have a slope of -5/2
So line is y= -5x/2 +b
Now set y= 4 and x = 0 to find b

Answer 3

In order to get the slope with two points given you have to use this formula...

m=y2-y1/x2-x1 (y1 and y2 are your y numbers from the two points, x1 and x2 are the x numbers.) m is going to be the slope.

m= -7+2/-1+8 (neg-neg=pos) (you have to use the points in the same order...I used the first point first for the y and the x)

m= -5/7 this is your slope

Slope intercept form is y-y1=m(x-x1)
(the y1 and x1 are the x and y points using only one set of points now. The m is the slope)

y+7= -5/7(x+7) To get rid of the fraction it is easier to multiply both sides by 7 (the denominator) and then distribute the right side.

7y+49= -5x-35 Now subtract 49 from both sides to get y by itself

7y= -5x-84 divide everything by 7 to get y by itself

y= -5/7x-12

Use everything I just gave you to do the same thing for the second problem. Unfortunately it is a matter of remembering the formulas! Hope this helps!

Good luck!

Answer 4

You should draw a graph.
The x axis is the parallel line. The y axis is the vertical line.
Slope is the y value divided by the x value.

Rise/Run Y rises (vertical) and X runs (horizontal).

Just read and reread until it sinks in. Eventually, it will. I had a hard time with this myself initially.

(-1, -7) are 2 points on a plane. The first value given is the x value and the second value is the y value.