Math  /  Algebra

QuestionJohn 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, yy, after xx weeks:
Which equation best models the relationship between xx and yy ? ( 5 points) 1) y=5x+25y=-5 x+25 2) y=25x+125y=-25 x+125 3) y=25x+175y=-25 x+175 4) y=5x+125y=-5 x+125

Studdy Solution

STEP 1

1. The graph represents a linear relationship between the number of weeks, x x , and the number of pages left to read, y y .
2. The line on the graph starts at the point (0, 175) and ends at the point (7, 0).
3. We need to find the equation of the line in the form y=mx+b y = mx + b , where m m is the slope and b b is the y-intercept.

STEP 2

1. Identify the y-intercept from the graph.
2. Calculate the slope of the line.
3. Write the equation of the line using the slope and y-intercept.
4. Compare the derived equation with the given options to find the best match.

STEP 3

Identify the y-intercept from the graph. The y-intercept is the point where the line crosses the y-axis. From the graph, the line starts at (0, 175).
Thus, the y-intercept b b is 175.

STEP 4

Calculate the slope m m of the line using the formula:
m=y2y1x2x1 m = \frac{y_2 - y_1}{x_2 - x_1}
Using the points (0, 175) and (7, 0):
m=017570=1757=25 m = \frac{0 - 175}{7 - 0} = \frac{-175}{7} = -25

STEP 5

Write the equation of the line using the slope m m and y-intercept b b :
y=25x+175 y = -25x + 175

STEP 6

Compare the derived equation y=25x+175 y = -25x + 175 with the given options:
1) y=5x+25 y = -5x + 25 2) y=25x+125 y = -25x + 125 3) y=25x+175 y = -25x + 175 4) y=5x+125 y = -5x + 125
The equation y=25x+175 y = -25x + 175 matches option 3.
The equation that best models the relationship is:
y=25x+175 \boxed{y = -25x + 175}

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