Answer:
f(x)=6x-5
Step-by-step explanation:
The common difference is 6 because of the following:
7-1=6
13-7=6
19-13=6
25-19=6
31-25=6
The common difference is the slope of the linear equation.
Slope-intercept form for a function is f(x)=mx+b where m is the slope and b is the y-intercept.
We just found m=6.
f(x)=6x+b
The y-intercept happens at x=0.
I'm referring to looking at the data as:
x | y
1 | 1
2| 7
3| 13
4| 19
5| 25
6| 31
We can use the pattern that y goes up by 6 as x goes up by 1 to find what happens at x=0.
x| y
0 1-6=-5
So b=-5.
So the function that we are looking for is f(x)=6x-5.
Answer:
2. y = -1/2x - 1
Step-by-step explanation:
First we want to find the slope of the line.
To find the slope of the line, we use the slope formula: (y₂ - y₁) / (x₂ - x₁)
Plug in these values using two points (-4, 1) & (2, -2)
(-2 - 1) / (2 - (-4))
Simplify the parentheses.
= (-2 - 1) / (2 + 4)
= (-3) / (6)
Simplify the fraction.
-3/6
= -1/2
This is your slope. Plug this value into the standard slope-intercept equation of y = mx + b.
y = -1/2x + b
b is the y-intercept when the line crosses the y-axis.
From the graph, we can see that the point on the y-axis is (0, -1)
Therefore, b is -1.
Plug this into the equation.
y = -1/2x - 1
Hope this helps!
Vertical angles:
Vertical Angles are the angles opposite each other when two lines cross.
https://www.mathsisfun.com/geometry/vertical-angles.html
The link has a visual of vertical angles.
Adjacent Angles:
Adjacent angles are two angles that share a common vertex point and a common side. They basically sit right next to each other.
https://www.mathsisfun.com/geometry/adjacent-angles.html
The link has a visual of adjacent angles.
Complementary Angles:
Two angles whose measures add to 90º.
Basically, together they make a right angle.
Supplementary Angles:
Two angles whose measures add to 180º.
Basically, together they form a straight line.
We know that 1 cup contains 8 fluid ounces, so we can solve this by setting up a proportion:
1 cup/8 fl oz. = x cups/128 fl oz.
(1)(128)=8x
128=8x
x=16 cups