Final answer:
The equation 2x + y = 10 can be written in slope-intercept form as y = 10 - 2x. The slope represents the rate at which Allie reduces the number of miles left to jog each day, and the y-intercept represents the initial number of miles left on day 0.
Step-by-step explanation:
To write the equation 2x + y = 10 in slope-intercept form, we need to solve for y. First, subtract 2x from both sides of the equation to isolate y: y = 10 - 2x. Now, the equation is in the form y = mx + b, where m represents the slope and b represents the y-intercept. In this case, the slope is -2 and the y-intercept is 10.
In the context of the situation, the slope (-2) represents the rate at which Allie is reducing the number of miles left to reach her goal each day. The y-intercept (10) represents the number of miles Allie would have left to jog this week if she started with a total of 10 miles left on day 0.
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