Answer:
The equation of the line that passes through the points (0, 3) and (5, -3) is 
.
Step-by-step explanation:
From Analytical Geometry we must remember that a line can be formed after knowing two distinct points on Cartesian plane. The equation of the line is described below:
(Eq. 1)
Where:
- Independent variable, dimensionless.
- Dependent variable, dimensionless.
- Slope, dimensionless.
- y-Intercept, dimensionless.
If we know that 
and 
, the following system of linear equations is constructed:
(Eq. 2)
(Eq. 3)
The solution of the system is: , 
. Hence, we get that equation of the line that passes through the points (0, 3) and (5, -3) is .
Answer:
Step-by-step explanation:
add 4 on both sides
leaves you with 15 on the right side
you then divide by negative 2
since you divide by a negative you have to switch the sign
Answer:
£0.33
Step-by-step explanation:
Rhianna has £25.
1 plant costs £3.95, she buys all of them.
25/3.95 = 6.329114
She buys a total of 6 plants.
With £0.33 remaining, which is the change.
This graph has a horizontal asymptote so it is an exponential graph. It also passes through two points (0,-2) and (1,3). The horizontal asymptote is at y=-3.
The unchanged exponential equation is y=a(b)^x +k
For exponential equations, k is always equal to the horizontal asymptote, so k=-3.
You can check this with the ordered pair (0,-2). After that plug in the other ordered pair, (1,3).
This gives you 3=a(b)^1 or 3=ab. If you know the base the answer is simple as you just solve for a.
If you don't know the base at this point you have to sort of guess. For example, let's say both a and b are whole numbers. In that case b would have to be 3, as it can't be 1 since then the answer never changes, and a is 1. Then choose an x-value and not exact corresponding y-value. In this case x=-1 and y= a bit less than -2.75. Plug in the values to your "final" equation of y=(3)^x -3.
So -2.75=(3^-1)-3.
3^-1 is 1/3, 1/3-3 is -8/3 or -2.6667 which is pretty close to -2.75. So we can say the final equation is y=3^x -3.
Hope this helps! It's a lot easier to solve problems like these given either more points which you can use system of equations with, or with a given base or slope.
πR³
