A straight-line graph with two axis crossings gives you a quick route to its equation. Each crossing is an intercept: one coordinate is zero. Write the line using its two intercepts, then clear the denominators to match the choices. Keep the coordinates in order so the strawberry count stays with and the banana count stays with .
Hints
- Hint 1
An intercept is where a line meets an axis. At the horizontal crossing, ; at the vertical crossing, . Read both points from the graph, keeping strawberries on the horizontal axis.
- Hint 2
In intercept form, a line crossing the axes at and is written . Put each crossing under the matching variable. What belongs under ?
- Hint 3
Multiply every term of the fraction equation, including the , by a number divisible by both denominators. This gives an equivalent equation with whole-number coefficients that you can match to a choice.
Step-by-step
Write the line from its intercepts
Step 1Read the two axis crossings
No Desmos needed. The graph gives both axis crossings directly. The line meets the vertical axis at and the horizontal axis at . These are its intercepts: the first means 50 banana cartons and no strawberry cartons; the second means 80 strawberry cartons and no banana cartons.
- Step 2
Write the line using those crossings
For a straight line, divide each variable by the value where the line meets its axis, then add the fractions. In intercept form, that gives:
Put each axis crossing under its own variable. Both points make this equation true, and two distinct points determine the line.
- Step 3
Match the equation to a choice
Use , which is divisible by both and . Multiply every term by :
Simplify the fractions:
So this equation represents the graphed relationship between strawberry and banana cartons. Choice A.