Answer:
21
Step-by-step explanation:
"Rate of change" is another name for "slope".
In the table, every time 'x' increases by 2, 'y' also increases by 2.
So the rate of change (slope) of the function in the table is
(change in 'y') / (change in 'x') = 2/2 = 1 .
The rate of change (slope) in the function y = x + 4 is
the coefficient (number before) the 'x'. That's also ' 1 '.
So t<span>he rate of change in the function y = x + 4 is the same as (equal to)
the rate of change of the function represented in the table.</span>
Step 1
<u>Find the slope of the line PQ</u>
we know that
the formula to calculate the slope between two points is equal to
![m=\frac{y2-y1}{x2-x1}](https://tex.z-dn.net/?f=m%3D%5Cfrac%7By2-y1%7D%7Bx2-x1%7D)
we have
![P(-3,-3)\\Q(3,-1)](https://tex.z-dn.net/?f=P%28-3%2C-3%29%5C%5CQ%283%2C-1%29)
substitute the values
![m=\frac{-1+3}{3+3}](https://tex.z-dn.net/?f=m%3D%5Cfrac%7B-1%2B3%7D%7B3%2B3%7D)
![m=\frac{2}{6}](https://tex.z-dn.net/?f=m%3D%5Cfrac%7B2%7D%7B6%7D)
![m=\frac{1}{3}](https://tex.z-dn.net/?f=m%3D%5Cfrac%7B1%7D%7B3%7D)
Step 2
Find the equation of the line that passes through point R ans is parallel to line PQ
we know that
If two lines are parallel, then their slopes are the same
The equation of the line into point-slope form is equal to
![y-y1=m(x-x1)](https://tex.z-dn.net/?f=y-y1%3Dm%28x-x1%29)
we have
![m=\frac{1}{3}](https://tex.z-dn.net/?f=m%3D%5Cfrac%7B1%7D%7B3%7D)
![(x1,y1)=R(1,1)](https://tex.z-dn.net/?f=%28x1%2Cy1%29%3DR%281%2C1%29)
substitute the values
![y-1=\frac{1}{3}(x-1)](https://tex.z-dn.net/?f=y-1%3D%5Cfrac%7B1%7D%7B3%7D%28x-1%29)
Step 3
we know that
The point on the y-axis that is on the line
is equal to the y-intercept of the line
The y-intercept is the value of y when the value of x is equal to zero
so
For
find the value of y in the linear equation
![y-1=\frac{1}{3}(0-1)](https://tex.z-dn.net/?f=y-1%3D%5Cfrac%7B1%7D%7B3%7D%280-1%29)
![y-1=-\frac{1}{3}](https://tex.z-dn.net/?f=y-1%3D-%5Cfrac%7B1%7D%7B3%7D)
![y=1-\frac{1}{3}](https://tex.z-dn.net/?f=y%3D1-%5Cfrac%7B1%7D%7B3%7D)
![y=\frac{2}{3}](https://tex.z-dn.net/?f=y%3D%5Cfrac%7B2%7D%7B3%7D)
The point that is on the y-axis is ![(0,\frac{2}{3})](https://tex.z-dn.net/?f=%280%2C%5Cfrac%7B2%7D%7B3%7D%29)
therefore
<u>the answer is the option A</u>
![(0,\frac{2}{3})](https://tex.z-dn.net/?f=%280%2C%5Cfrac%7B2%7D%7B3%7D%29)
see the attached figure to better understand the problem
Answer:
yes, y=2x-3 is linear
2x - y = 3 Standard Form
Step-by-step explanation:
since both the 'x' and 'y' variables have one as their exponents then this represents a linear equation
standard form: Ax + By = C
y = 2x - 3
subtract 2x from each side to get:
-2x + y = -3
divide each term by -1 to get (this is done so the leading coefficient is not negative)
2x - y = 3 Standard Form