Question

this graph shows how the number of plants finn can have in his backyard is related to the number of seed packets he purchases.
plants in finns backyard
with 5 seed packets, how many total plants can finn have in his backyard?
plants

Explanation:

Step1: Identify the x - value

The x - axis represents the number of seed packets. We are given that the number of seed packets \(x = 5\).

Step2: Find the corresponding y - value

The y - axis represents the total number of plants. To find the number of plants when \(x = 5\), we look at the graph. The line passes through the point where \(x = 5\). From the graph, when \(x=5\), we can see that the y - value (number of plants) can be calculated using the slope - intercept form of a line \(y=mx + b\). First, find the slope \(m\). The y - intercept \(b = 50\) (when \(x = 0\), \(y=50\)). Let's take two points, say \((0,50)\) and \((6,98)\) (approximate from the graph, but we can also see the pattern). The slope \(m=\frac{y_2 - y_1}{x_2 - x_1}=\frac{98 - 50}{6 - 0}=\frac{48}{6} = 8\). So the equation is \(y=8x + 50\). When \(x = 5\), \(y=8\times5+50=40 + 50=90\)? Wait, no, looking at the graph, when \(x = 0\), \(y = 50\), when \(x = 1\), \(y=58\) (since slope is 8, \(50+8 = 58\)), \(x = 2\), \(y = 66\), \(x = 3\), \(y=74\), \(x = 4\), \(y = 82\), \(x = 5\), \(y=90\)? Wait, no, the graph shows that when \(x = 5\), the y - value is 90? Wait, no, let's check the grid. The y - axis has 50 at \(x = 0\), then each grid line for y is 10, and for x is 1. The line goes from (0,50) to (6,98) (approx), but actually, looking at the graph, when \(x = 5\), the point on the line is at \(y = 90\)? Wait, no, let's count the rise over run. From (0,50) to (1,58) (rise 8, run 1), (2,66), (3,74), (4,82), (5,90), (6,98). So when \(x = 5\), \(y=90\)? Wait, no, the initial y - intercept is 50, slope 8. So \(y=8x + 50\). For \(x = 5\), \(y=8\times5+50=40 + 50 = 90\). Alternatively, by looking at the graph, when the number of seed packets (x) is 5, we move up from \(x = 5\) on the x - axis until we hit the line, then left to the y - axis. The y - axis at that point is 90? Wait, no, the graph's y - axis starts at 50, then each square is 10? Wait, no, the y - axis has 50, 60, 70, 80, 90, 100. The line goes from (0,50) to (6,98) (close to 100). Wait, maybe my slope calculation is wrong. Let's take (0,50) and (6,98), the difference in y is 48, difference in x is 6, so slope is 8. So for \(x = 5\), \(y=50+8\times5=50 + 40=90\). So the number of plants is 90.

Answer:

90