Errol's bike ride from home to school can be modeled by the equation d(t) = - 1/4 * t + 2 where d(t) is his distance from school
in miles, at t minutes. Errol's friend Daniel lives 4 miles away from school. It takes Daniel twice as long to get to school if he bike rides at the same pace as Errol. What can be said about the graph of the equation that models Daniel's bike rides?
1 answer:
Answer:
Daniel's equation will have a vertical translation by 2 units in the positive direction.
Step-by-step explanation:
Errol's bike ride can be modeled by the equation,
Slope of the equation =
Here slope defines the rate of change of distance from Errol's house.
Y-intercept = 2, which represents the distance of the school from his home.
Let the equation that represents the equation is,
d(t) = mt + b
Errol's friend Daniel lives 4 miles away from school that means y intercept of the equation (b) = 4
Since Daniel drives his bike at the same pace as Errol, slope will be same.
Equation that models the distance will be
If we compare both the equations, slopes are same but y-intercepts have a difference of 2 units
Therefore, the graph from the Daniel's equation will have a vertical translation by 2 units in the positive direction.
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That is not correct. I will help you. Begin by subtracting the 9x from both sides, like this: 9x - 9x + 2y = 6 - 9x. That simplifies to 2y = -9x + 6. Now divide both sides by 2 to get y all alone, like this: 
. That reduces down to 
. That is slope-intercept form. y = mx + b.
Answer:
<u><em>(-1,1)</em></u>
Step-by-step explanation:
We can solve this by either graphing and finding ther point the lines intersect, or mathematically, I'll do both.
<u>Graphing:</u>
<u>Mathematically:</u>
−2x + 4y = 6
y = 2x + 3
See the attached graph. The lines intersect at (-1,1)
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I'll rearrange the first equation (to make it easier for me):
−2x + 4y = 6
4y = 2x + 6
y = (1/2)x + 1.5
Now lets substitute the second equation into the first so that we can eliminate y:
y = 2x + 3
[(1/2)x + 1.5] = 2x + 3
- (3/2)x = (3/2)
x = -1
If x = -1:
y = 2(-1) + 3
y = 1
The solution is x = -1 and y = 1, or (-1,1)
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Both approaches give us (-1,1), the solution to the system of equations. It is the only point that satisfies both equations.
