Answer:
linear equation
Step-by-step explanation:
43x + 4 = y is known as <u>a linear equation since its graph is a straight line</u>.
You can certainly start out that way, but when you solve that equation for x, it's a little more complex than if you started with the other equation. I usually start with the most simple equation first. Let's take the first equation and solve for y... that will leave us without any fractions to deal with.
2x + y = -14
y = -14 - 2x
Now we have a y value and we can substitute it back into the other equation. So we will replace y in the second equation with (-14 - 2x).
That will leave us with just the x as a variable and we can solve for x.
7x - 4y = -19
7x - 4(-14 - 2x) = -19 multiply the -4 through the parentheses
7x + 56 + 8x = -19 combine like terms
15x + 56 = -19 subtract 56 from each side
15x = -75 divide each side by 15
x = -5
Now we have a value for x that we can substitute back into either of the original equations and then solve for y. I usually go with the easier equation, but it doesn't matter. Let's use the first one...
2x + y = -14
2(-5) + y = -14 multiply the 2 through the parentheses
-10 + y = -14 add 10 to each side
y = -4
So your ordered pair is
(-5, -4)
That is where the 2 lines are equal to one another, so that's the point where they they intersect.
Note*** You can start these problems with either equation and solving for either x or y... it doesn't matter. After you substitute the values into the other equation it will work out the same.
Answer:
Linear functions.
Exponential functions.
Step-by-step explanation:
An example of an arithmetic sequence is 1, 3, 5, 7, common difference is 2 and is modelled by the linear function
1 + 2(n -1).
A geometric sequence might be 2, 4, 8, 16 where there is a common ratio of 2 and is modelled by 2.(2)^n-1).
Answer:
The equation of the line that passes through the point (4,7) and has a slope of 0 will be:
Step-by-step explanation:
As we know the equation of a line in a slope-intercept form of an equation is
![y = mx + b](https://tex.z-dn.net/?f=y%20%3D%20mx%20%2B%20b)
Here,
so
substituting the point (4,7) and slope m=0
![y = mx + b](https://tex.z-dn.net/?f=y%20%3D%20mx%20%2B%20b)
![7=0(4)+b](https://tex.z-dn.net/?f=7%3D0%284%29%2Bb)
![7=0+b](https://tex.z-dn.net/?f=7%3D0%2Bb)
![b=7](https://tex.z-dn.net/?f=b%3D7)
Therefore, the equation of the line that passes through the point (4,7) and has a slope of 0 will be:
![y = mx + b](https://tex.z-dn.net/?f=y%20%3D%20mx%20%2B%20b)
![y=0x+7](https://tex.z-dn.net/?f=y%3D0x%2B7)
![y=7](https://tex.z-dn.net/?f=y%3D7)