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) ]
=========================================
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.
X<-7 so the answer would be greater*
Multiply -8 on both sides
n + 2 = 32 Subtract 2 on both sides
n + 2 - 2 = 32 - 2
n = 30
Given:
Width of a garden = 10 feet
Length of the garden = 14 feet
Area of the garden and the walkway together = 396 square feet.
To find:
The width of the walkway.
Solution:
A cement walkway is added around the outside of the garden.
Let x be the width of the walkway.
The width of the garden with walkway = 10+2x
The length of the garden with walkway = 14+2x
Area of a rectangle is
Area of garden and the walkway together is
Divide both sides by 4.
Splitting the middle term, we get
Using zero product property, we get
Width of walkway cannot be negative. So, x=4.
Therefore, the width of the walkways is 4 feet.
