LaMarcus is 1400 miles away from home when he starts driving at a rate of 65 miles per hour. As he drives, his distance from home can be modeled by y=65x+1400𝑦=65𝑥+1400 , where x is the time in hours since he left. Bianca is also traveling away from her home, and the function representing her distance from home is parallel to the function representing LaMarcus’s distance. After 5 hours, Bianca is 1525 miles from home. Which function represents Bianca’s distance from home over time?
Question
LaMarcus is 1400 miles away from home when he starts driving at a rate of 65 miles per hour. As he drives, his distance from home can be modeled by y=65x+1400𝑦=65𝑥+1400 , where x is the time in hours since he left. Bianca is also traveling away from her home, and the function representing her distance from home is parallel to the function representing LaMarcus’s distance. After 5 hours, Bianca is 1525 miles from home. Which function represents Bianca’s distance from home over time?
Solution
The problem states that the function representing Bianca's distance from home is parallel to the function representing LaMarcus's distance. This means that the rate at which they are driving is the same, so the slope of the function, or the coefficient of x, is the same for both functions. In this case, it is 65.
The function representing LaMarcus's distance from home is y = 65x + 1400.
For Bianca, we know that after 5 hours, she is 1525 miles from home. We can substitute these values into the equation to find the y-intercept (b).
1525 = 65(5) + b 1525 = 325 + b b = 1525 - 325 b = 1200
So, the function representing Bianca's distance from home over time is y = 65x + 1200.
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