Question

6
y = 40x + 20

Explanation:

Step1: Analyze the equation and graph

The equation given is \( y = 40x + 20 \), and we have a graph with x - axis from 0 - 10 and y - axis from 0 - 240. Let's check the y - intercept. For the equation \( y=mx + b \), the y - intercept \( b = 20 \), but the graph seems to have a y - intercept at 40. Wait, maybe there is a mis - check. Wait, let's check a point. Let's take \( x = 0 \), the equation gives \( y=20 \), but the graph at \( x = 0 \) has \( y = 40 \). Wait, maybe the graph is for a different equation? Wait, maybe we need to check the slope. The slope of the equation \( y = 40x+20 \) is 40. Let's calculate the slope from the graph. Take two points, say (0,40) and (1,80). The slope \( m=\frac{80 - 40}{1-0}=40 \). Oh, so the graph has a y - intercept of 40, but the equation is \( y = 40x + 20 \). Wait, maybe there is a typo, but if we consider the slope, the graph has a slope of 40. Let's verify with \( x = 1 \): equation gives \( y=40(1)+20 = 60 \), but graph at \( x = 1 \) is 80. Wait, no, maybe the graph's y - axis is misread. Wait, the graph's y - axis: at \( x = 0 \), y is 40, \( x = 1 \), y is 80, \( x = 2 \), y is 120, so the equation of the graph is \( y = 40x+40 \)? But the given equation is \( y = 40x + 20 \). Wait, maybe the question is to check if the graph matches the equation. Let's check the y - intercept. The equation \( y = 40x+20 \) has y - intercept 20, the graph has y - intercept 40. So the graph does not match the equation \( y = 40x + 20 \). But if we assume that we need to find the equation of the graph: using two points (0,40) and (1,80), slope \( m=\frac{80 - 40}{1 - 0}=40 \), so equation is \( y=40x + 40 \). But the given equation is \( y = 40x+20 \). Alternatively, maybe the graph is correct and the equation has a typo. But if we proceed with the graph, let's say we want to find y when \( x = 5 \). For the graph, using \( y = 40x+40 \), when \( x = 5 \), \( y=40\times5 + 40=240 \)? No, at \( x = 5 \), the graph's y is 160? Wait, no, the graph at \( x = 5 \) is 160? Wait, the y - axis: 40, 80, 120, 160, 200, 240. So at \( x = 0 \), y = 40; \( x = 1 \), y = 80; \( x = 2 \), y = 120; so the equation is \( y = 40x+40 \). The given equation is \( y = 40x + 20 \), so the graph and the equation do not match. But maybe the question is to find the equation of the graph. Let's do that.

Step2: Find the equation of the line from the graph

1. Identify two points on the graph: (0, 40) and (1, 80) (we can see from the grid).
2. Calculate the slope \( m=\frac{y_2 - y_1}{x_2 - x_1}=\frac{80 - 40}{1 - 0}=40 \).
3. The y - intercept \( b \) is the value of y when \( x = 0 \), which is 40. So the equation of the graph is \( y = 40x+40 \). The given equation is \( y = 40x + 20 \), so they differ in the y - intercept.

Answer:

The graph does not match the equation \( y = 40x + 20 \). The equation of the graph is \( y=40x + 40 \) (if we derive from the graph's points (0,40) and (1,80)).