A graph of two lines represents a system of equations; its solution is the point where they cross. Trace both lines to the shared grid point, then read the first coordinate as and the second as . Use the coordinates in the order the requested ratio demands. Reversing the ratio or ignoring a negative coordinate changes the value.
Hints
- Hint 1
An intersection is a point on both lines, so you don't need to write equations if you can find their shared grid point. Trace the first line from where it crosses the -axis. Where does it meet the second line?
- Hint 2
An ordered pair puts the horizontal coordinate first and the vertical coordinate second. Once you find the crossing, label each coordinate before making the requested fraction.
- Hint 3
In , the top number is , the second coordinate of the intersection. A point below the -axis has a negative -coordinate, so keep that sign when you divide.
Step-by-step
Read the intersection from the graph
Step 1Trace the first line to a grid point
No Desmos needed. Read the shared point from the graph. The first bold line moves squares right and squares up from to , so it rises one square for each square right. Moving squares right from puts it at .
- Step 2
Identify the solution
The second bold line also passes through , so both lines meet there. Their intersection is the solution, . In an ordered pair, comes first and comes second.
- Step 3
Find the requested ratio
The question asks for divided by , not the reverse. Use and from the intersection:
So the value of is . Choice A.