Question

to grow properly, a tomato plant needs 1.5 square feet of soil, and a broccoli plant needs 2.25 square feet of soil. the graph shows the different combinations of broccoli and tomato plants in an 18 - square - foot plot of soil.*
match each point to the statement that describes it.
a. point a

1. the soil is fully used when six tomato plants and four broccoli plants are planted.

b. point b

1. only broccoli was planted, but the plot is fully used and all plants can grow properly.

c. point c

1. after three tomato plants and two broccoli plants were planted, there is still extra space in the plot.

d. point d

1. with four tomato plants and six broccoli plants planted, the plot is overcrowded.

Explanation:

Step1: Analyze each statement

• Statement 1: "The soil is fully used when six tomato plants and four broccoli plants are planted." This means the point is on the line (representing full - soil usage). Looking at the graph, point A is on the line.
• Statement 2: "Only broccoli was planted, but the plot is fully used and all plants can grow properly." If only broccoli is planted (tomato plants \(t = 0\)), and the plot is fully used (on the line). But none of the points \(A\), \(B\), \(C\), \(D\) have \(t = 0\). However, if we consider the general concept of the line equation \(1.5t+2.25b=18\) (where \(t\) is the number of tomato plants and \(b\) is the number of broccoli plants). If \(t = 0\), then \(b=\frac{18}{2.25}=8\). But among the given points, point \(B\) is below the line (not fully - used if we consider non - zero \(t\) and \(b\) combination. Wait, re - check: The line equation \(1.5t + 2.25b=18\). For point \(B\), assume \(t = 3\) and \(b = 2\), \(1.5\times3+2.25\times2=4.5 + 4.5=9

eq18\). Wait, wrong approach. The line represents the boundary of full - soil usage. Point \(B\) is inside (below) the line (under - utilized), but if we consider the statement "Only broccoli was planted... fully used", no, but if we assume the problem's intention: The line \(1.5t+2.25b = 18\). For statement 2, if \(t = 0\), \(b = 8\) (not a given point). But if we consider the combination: For statement 2, if we assume the problem has a typo and means a non - zero combination where the plot is fully used. Wait, no. Wait, the line \(1.5t+2.25b=18\). For point \(B\), if we assume \(t = 2\) and \(b = 2\) (approximate from the graph), \(1.5\times2+2.25\times2=3 + 4.5 = 7.5
eq18\). Wait, wrong. Let's use the fact that the line is the full - usage. Point \(A\): If \(t = 6\) and \(b = 4\), \(1.5\times6+2.25\times4=9 + 9=18\). Point \(C\): Assume \(t = 3\) and \(b = 6\) (from the line - like position), \(1.5\times3+2.25\times6=4.5+13.5 = 18\). But statement 3: "After three tomato plants and two broccoli plants were planted, there is still extra space in the plot." If \(t = 3\) and \(b = 2\), \(1.5\times3+2.25\times2=4.5 + 4.5=9\lt18\) (extra space), which is point \(B\). Statement 4: "With four tomato plants and six broccoli plants planted, the plot is overcrowded." \(1.5\times4+2.25\times6=6 + 13.5=19.5\gt18\) (overcrowded), which is point \(D\).

Answer:

a. Point A; b. Point B; c. Point C; d. Point D