Lesson 10

Select all of the ordered pairs $(x,y)$ that are solutions to the linear equation $2x+3y=6$.

$(0,2)$

$(0,6)$

$(2,3)$

$(3,\text-2)$

$(3,0)$

$(6,\text-2)$

The graph shows a linear relationship between $x$ and $y$.

$x$ represents the number of comic books Priya buys at the store, all at the same price, and $y$ represents the amount of money (in dollars) Priya has after buying the comic books.

1. Find and interpret the $x$- and $y$-intercepts of this line.
    
2. Find and interpret the slope of this line.
    
3. Find an equation for this line.
4. If Priya buys 3 comics, how much money will she have remaining?

Match each equation with its three solutions.

A container of fuel dispenses fuel at the rate of 5 gallons per second. If $y$ represents the amount of fuel remaining in the container, and $x$ represents the number of seconds that have passed since the fuel started dispensing, then $x$ and $y$ satisfy a linear relationship.

In the coordinate plane, will the slope of the line representing that relationship have a positive, negative, or zero slope? Explain how you know.

A sandwich store charges a delivery fee to bring lunch to an office building. One office pays $33 for 4 turkey sandwiches. Another office pays $61 for 8 turkey sandwiches. How much does each turkey sandwich add to the cost of the delivery? Explain how you know.