can someone write out the equations so i can solve it. Please...
#1
A biologist recorded 9 snakes on 21 acres in one area and 13 snakes on 47 acres in another area. Let y be the number of snakes in x acres. Write this one in a linear equation for the number of snakes.
The straight line that goes through both points (21,9) and (47,13) would have slope m = (4/26) = 2/13
The equation of the line would be
(y - 9) = (2/13) (x - 21)
y = (2/13)x + 9 - 42/13
= (2/13)x + 75/13
A more likely formula would be one without a constant (since the numnber of snakes shold be zero when tha area is zero) That is a "best-fit" straight line. There are other ways to calculate that.
thats right i completely forgot to set them up as points and solve from there duhhh to me . Thank you so much for bringing it out.
13y+2x+75
To solve the problem, you need to set up a linear equation using the given information.
First, let's define the variables:
- Let x represent the number of acres.
- Let y represent the number of snakes.
Next, identify two points on the line:
Point 1: (x₁, y₁) = (21, 9)
Point 2: (x₂, y₂) = (47, 13)
The slope of the line can be calculated using the formula:
m = (y₂ - y₁) / (x₂ - x₁)
Substituting the values:
m = (13 - 9) / (47 - 21)
m = 4 / 26
m = 2 / 13
Now that we have the slope, we can use the point-slope form of a line to write the equation:
(y - y₁) = m(x - x₁)
Substituting the values:
(y - 9) = (2/13)(x - 21)
You can simplify the equation by distributing the 2/13:
(y - 9) = (2/13)x - (2/13) * 21
Simplifying further:
y - 9 = (2/13)x - 42/13
To isolate y, add 9 to both sides of the equation:
y = (2/13)x + 9 - 42/13
Combining like terms:
y = (2/13)x + 75/13
So the linear equation representing the relationship between the number of snakes (y) and the number of acres (x) is:
y = (2/13)x + 75/13
However, keep in mind that this equation assumes a constant rate of snakes per acre. In reality, the relationship may not be perfectly linear, so this equation should be treated as an approximation.