Math  /  Algebra

QuestionThe Sterns initially drove some miles before they made a plan of driving set miles each day. Days 3,4 , and 5 are displayed on the graph.
Determine the initial amount of miles the Sterns drove before making a plan. \square miles

Studdy Solution

STEP 1

1. The Sterns initially drove some miles before following a daily driving plan.
2. The graph shows the total miles driven on days 3, 4, and 5.
3. The points on the graph are (3, 785), (4, 996), and (5, 1207).
4. The x-axis represents days, and the y-axis represents total miles driven.
5. We need to determine the initial miles driven before day 1.

STEP 2

1. Understand the relationship between days and total miles driven.
2. Determine the daily miles driven based on the graph.
3. Calculate the initial miles driven before day 1.

STEP 3

Understand the relationship between days and total miles driven. The points on the graph suggest a linear relationship between the number of days and the total miles driven.

STEP 4

Determine the daily miles driven based on the graph. Calculate the slope (rate of change) between any two points to find the daily miles driven.
Using points (3, 785) and (4, 996):
Slope=99678543=2111=211 \text{Slope} = \frac{996 - 785}{4 - 3} = \frac{211}{1} = 211
This indicates that the Sterns drove 211 miles per day.

STEP 5

Calculate the initial miles driven before day 1. Use the point-slope form of a line to find the y-intercept, which represents the initial miles.
Using the point (3, 785) and the slope 211:
y785=211(x3) y - 785 = 211(x - 3)
Substitute x=0 x = 0 to find the y-intercept (initial miles):
y785=211(03) y - 785 = 211(0 - 3) y785=633 y - 785 = -633 y=785633 y = 785 - 633 y=152 y = 152
The initial amount of miles the Sterns drove before making a plan is:
152 \boxed{152}

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