+2446 1. Days
The number of days that pass cannot be controlled as one cannot simply stop or speed up time, so this is the independent variable.
2. Pounds of Dog Food
The amount of pounds of dog food can be controlled by consuming less per day, so this is the dependent variable. Also, the number of days that pass linearly influences the amount of pounds remaining.
3.
There are a few methods to calculate the slope here, but I will simply select two points on the provided graph, which will be \((30,0)\) and \((0,40)\). Use the slope formula to calculate the slope.
\(m=\frac{0-40}{30-0}=\frac{-40}{30}=-\frac{4}{3}\)
This is the slope.
4.
The y-intercept of this function is located at \((0,40)\). For this problem, this indicates the number of pounds of dog food originally in the bag before consumption.
5.
We already know the slope, and we already know the y-intercept, so it is relatively simple to craft the function using function notation. Just put the pieces together.
Let d = number of days
\(f(d)=-\frac{4}{3}d+40\)
6. To rewrite from function notation to slope-intercept notation, simply replace the \(f(d)\) with a y.
\(y=-\frac{4}{3}x+40\)
7.
The standard form of a line is written in the form \(Ax+By=C\) such that A,B, and C are all integers, A is equal to or greater than 0. Simply rearrange the equation written in slope-intercept form.
| \(y=-\frac{4}{3}x+40\) | Add 4/3x to both sides. |
| \(\frac{4}{3}x+y=40\) | Multiply by 3 on both sides to eliminate the fraction. |
| \(4x+3y=120\) | This equation meets all the guidelines for an equation in standard form. |
+2446 1. Days
The number of days that pass cannot be controlled as one cannot simply stop or speed up time, so this is the independent variable.
2. Pounds of Dog Food
The amount of pounds of dog food can be controlled by consuming less per day, so this is the dependent variable. Also, the number of days that pass linearly influences the amount of pounds remaining.
3.
There are a few methods to calculate the slope here, but I will simply select two points on the provided graph, which will be \((30,0)\) and \((0,40)\). Use the slope formula to calculate the slope.
\(m=\frac{0-40}{30-0}=\frac{-40}{30}=-\frac{4}{3}\)
This is the slope.
4.
The y-intercept of this function is located at \((0,40)\). For this problem, this indicates the number of pounds of dog food originally in the bag before consumption.
5.
We already know the slope, and we already know the y-intercept, so it is relatively simple to craft the function using function notation. Just put the pieces together.
Let d = number of days
\(f(d)=-\frac{4}{3}d+40\)
6. To rewrite from function notation to slope-intercept notation, simply replace the \(f(d)\) with a y.
\(y=-\frac{4}{3}x+40\)
7.
The standard form of a line is written in the form \(Ax+By=C\) such that A,B, and C are all integers, A is equal to or greater than 0. Simply rearrange the equation written in slope-intercept form.
| \(y=-\frac{4}{3}x+40\) | Add 4/3x to both sides. |
| \(\frac{4}{3}x+y=40\) | Multiply by 3 on both sides to eliminate the fraction. |
| \(4x+3y=120\) | This equation meets all the guidelines for an equation in standard form. |
