Given
[tex]\begin{gathered} 2x+3y=1470 \\ x\rightarrow\text{ number of sandwiches} \\ y\rightarrow\text{ number of wraps} \end{gathered}[/tex]
1) Solve for y to find the slope-intercept form, as shown below
[tex]\begin{gathered} \Rightarrow3y=1470-2x \\ \Rightarrow y=\frac{1470}{3}-\frac{2x}{3} \\ \Rightarrow y=-\frac{2}{3}x+490 \end{gathered}[/tex]
The slope-intercept form of the equation is y=-2x/3+490, where -2/3 is the slope and +490 is the y-intercept.
2) To graph the equation, start at (0,490), the y-intercept; then, move 3 units to the right for every 2 units down because the slope is -2/3.
For example, to the right of (0,490) we can find (0+3,490-2)=(3,488)
3) From part 1), notice that to the right of the equality there are only terms of x; then, we can rewrite it as shown below
[tex]\begin{gathered} y=f(x) \\ \Rightarrow f(x)=-\frac{2x}{3}+490 \end{gathered}[/tex]
The graph of f(x) is the number of wraps as a function of the number of sandwiches (x).
4)
5)
The slope of the two lines will be the same since the ratio cost of a sandwich to the cost of a wrap stays the same; in contrast, the value of the y-intercept will be different because the total profit is now $1593 rather than $1470
