Two questions are written to express how far a car can go when driving on different roads on road 1 the car can go 60 miles in two hours on road 2 the car can go 90 miles in four hours write an equation where y is the distance in miles and x is the time and hours to represent the motion of the faster car
Let's define the equation for the motion of the faster car:
On road 1, the car can go 60 miles in 2 hours. This can be represented as:
y = (60 miles / 2 hours) * x
On road 2, the car can go 90 miles in 4 hours. This can be represented as:
y = (90 miles / 4 hours) * x
Thus, the equation representing the motion of the faster car is:
y = 30x or y = 22.5x (depending on whether you want to round the values or not)
To represent the motion of the faster car, we can use the equation of a line:
y = mx + b
Where:
- y represents the distance in miles
- x represents the time in hours
- m represents the slope of the line
- b represents the y-intercept
In this case, let's assign the following variables:
- For road 1: y₁ = 60 miles, x₁ = 2 hours
- For road 2: y₂ = 90 miles, x₂ = 4 hours
To find the slope (m), we can use the formula:
m = (y₂ - y₁) / (x₂ - x₁)
Plugging in the values:
m = (90 - 60) / (4 - 2)
= 30 / 2
= 15
Now, let's find the y-intercept (b) by picking one of the points. Let's use road 1 (y₁, x₁):
60 = (15)(2) + b
60 = 30 + b
b = 60 - 30
b = 30
Therefore, the equation that represents the motion of the faster car is:
y = 15x + 30
To represent the motion of the faster car, we can use the equation of a straight line, which is in the form of y = mx + b, where y represents the distance in miles, x represents the time in hours, m represents the slope of the line, and b represents the y-intercept.
In this case, let's consider the faster car, which can go 90 miles in 4 hours. We can use this information to find the slope (m) of the line.
The slope of a line is calculated by dividing the change in the y-values (vertical change) by the change in the x-values (horizontal change). In this case, the change in distance (y) is 90 miles, and the change in time (x) is 4 hours.
So, the slope (m) can be calculated as:
m = (change in y) / (change in x)
= 90 miles / 4 hours
= 22.5 miles per hour
Now that we have the slope, we can write the equation using y = mx + b. Let's use the point (x, y) = (0, 0) on the line so that we can find the y-intercept (b).
By substituting the values x = 0 and y = 0 into the equation, we get:
0 = (22.5 miles/hour)(0) + b
0 = 0 + b
b = 0
Therefore, the equation representing the motion of the faster car is:
y = 22.5x + 0
or simply
y = 22.5x