You've got five different problems in this photo ... four on top and the word problem on the bottom ... and they're all exactly the same thing: Taking two points and finding the slope of the line that goes through them.
In every case, the procedure is the same.
If the two points are (x₁ , y₁) and (x₂ , y₂) , then
the slope of the line that goes through them is
Slope = (y₂ - y₁) / (x₂ - x₁) .
This is important, and you should memorize it.
#1). (8, 10) and (-7, 14)
Slope = (14 - 10) / (-7 - 8) = 4 / -15
#2). (-3, 1) and (-17, 2)
Slope = (2 - 1) / (-17 - -3) = (2 - 1) / (-17 + 3) = 1 / -14
#3). (-20, -4) and (-12, -10)
Slope = [ -10 - (-4) ] / [ -12 - (-20) ]
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The word problem:
This question only gives you one point on the graph,
and then it wants to know what's the slope ?
What are you going to do for another point ?
A "proportional relationship" always passes through the origin,
so another point on the line is (0, 0) .
Now you have two points on THAT line too, and you can easily
find its slope.
3(x + 2) + 4(x - 5) = 10
Use the distributive property:
3x + 6 + 4x - 20 = 10
Combine like terms:
7x -14 = 10
Add 14 to both sides:
7x = 24
Divide both sides by 7:
x = 24/7
Explanation:
1. CS ≅ HR, ∠CHS ≅ ∠HCR, ∠CSH ≅ ∠HRC — given
2. ∆CRH ~ ∆HSC — AA similarity theorem
3. ∠SCH ≅ ∠RHC — corresponding angles of similar triangles are congruent
4. CH ≅ HC — reflexive property of congruence
5. ∆CRH ≅ ∆HSC — SAS congruence theorem
6. CR ≅ HS — CPCTC
Answer:
z = 
Step-by-step explanation:
The ratio of corresponding sides are equal, that is
= 
( cross- multiply )
12z = 200 ( divide both sides by 12 )
z = 
=
Answer:
(2) (100, 300)
Step-by-step explanation:
One wave can be divided on 4 parts, as show on the picture.
Since a length of one whole wave equals 400, a length of each part is 
nanometers.
The height of the wave is decreasing on the second and on the third part, hence over the interval (100, 300).
