(05.03 MC)
Lisa reads an equal number of pages of a book every week. The graph below shows the number of pages of the book left to read, y, after x weeks:
A graph titled Lisas Book Reading shows Number of Weeks on the x-axis and Number of Pages Left on the y-axis. The scale on the x-axis shows numbers from 0 to 6 at increments of 1, and the scale on the y-axis shows numbers from 0 to 350 at increments of 50. A straight line joins the ordered pairs 0, 250 and 1, 200 and 2, 150 and 3, 100 and 4, 50 and 5, 0.
Which equation best models the relationship between x and y? (1 point)
y = −50x + 250
y = −5x + 50
y = −50x + 350
y = −5x + 250
Please help!! I am stuck on this question and I don't understand!!!!
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To find the equation that models the relationship between x and y based on the given graph, we need to identify the pattern and determine the slope-intercept form of the equation.
Looking at the graph, we can see that the number of pages decreases by a constant value each week. Let's calculate the change in y and x between consecutive points on the graph:
- From (0, 250) to (1, 200): The change in y is -50 (-250 to -200), and the change in x is 1.
- From (1, 200) to (2, 150): The change in y is also -50 (-200 to -150), and the change in x is 1.
Since the change in y is constant, we can conclude that the slope of the line (rate of change) is -50. Therefore, our equation will have a coefficient of -50x.
Now, let's find the y-intercept. We can observe from the graph that when x = 0, y = 250. Therefore, the y-intercept is 250.
Now we can write our equation using the slope-intercept form (y = mx + b):
y = -50x + 250
So, the correct equation that best models the relationship between x and y based on the graph is y = -50x + 250.
Thank you so much Reiny!!!! Means alot
Since the graph shows a straight line, it doesn't matter which pair of points we take, so
let's take the first two.
(0, 250) and (1,200).
The (0,250) is very useful since it shows the y-intercept to be 250
so our equation in the form y = mx + b
must be y = mx + 250
All we need is the slope!
slope = (200-250)/(1-0) = -50
so what do you think??