Harry reads equal numbers of pages of a book every week. The graph shows the number of pages of the book left to read, y, after x weeks:
api.agilixbuzz.com/Resz/~0.0gTVFcF5TD0SEUPK.m8w4YkR4g06lEVZbTrgvpLC_G_JJmLN4vuHvzL2UU/170405696,CBF,0,18,0/Assets/75484_53df9262/mjprealgebra_practice_m5_g10_c3.jpg
(the link to the graph)
Which equation best models the relationship between x and y? (1 point)
y = –5x + 55
y = –55x + 385
y = –5x + 275
y = –55x + 275
To find the equation that best models the relationship between x (weeks) and y (number of pages left to read), we need to analyze the slope and y-intercept of the graph.
Looking at the transformation of the graph, we can see that for every unit increase in x (week), the y (number of pages left) decreases by a certain amount. From the graph, it is clear that the number of pages left decreases at a constant rate as the weeks pass.
Now, let's analyze the options:
1. y = –5x + 55: This equation has a slope of -5 and a y-intercept of 55. But looking at the graph, it is evident that the slope is steeper than -5. This equation is not the best fit.
2. y = –55x + 385: This equation has a slope of -55 and a y-intercept of 385. However, the slope defined in this equation is much steeper than what we observe in the graph. Therefore, this equation is not the best fit either.
3. y = –5x + 275: This equation has a slope of -5 and a y-intercept of 275. The slope matches the rate of decrease in the graph, and the y-intercept is close to where the line intersects the y-axis on the graph. This equation seems like a good fit.
4. y = –55x + 275: This equation has a slope of -55 and a y-intercept of 275. As mentioned earlier, the observed slope in the graph is not as steep as -55. Therefore, this equation is not the best fit.
Based on the analysis, the equation that best models the relationship between x and y is y = –5x + 275.