Please I'm stuck!!!!!
A person is driving a car on a straight road. The graph shows the distance in y miles that the individual is from home after x hours.
the graph has the following points
(1, 40) and (3, 90)
Find the slope intercept of the line
y = ____x + ______
How fast is the car traveling?
_______ Miles per hour.
(Type and integer or decimal)
How far was the individual from home initally?
________ miles
(Type and integer or decimal)
How far was the individual from home after 3 hours and 15 minutes?
_________ miles
(Type in integer or decimal)
I am unsure how to solve the last couple of parts to this problem.
Help!!!
To find the slope-intercept form of the line, we need to calculate the slope and the y-intercept using the given points (1, 40) and (3, 90).
Step 1: Calculate the slope (m):
The formula for calculating the slope (m) is: m = (change in y) / (change in x)
In this case, (change in y) = 90 - 40 = 50 and (change in x) = 3 - 1 = 2.
So, m = 50 / 2 = 25.
Step 2: Calculate the y-intercept (b):
We know that the point (1, 40) lies on the line. We can substitute these values into the slope-intercept form (y = mx + b) and solve for b:
40 = 25 * 1 + b
40 = 25 + b
b = 40 - 25 = 15.
Therefore, the slope-intercept form of the line is y = 25x + 15.
Now, let's move on to the next question.
To find how fast the car is traveling, we need to determine the slope of the line. We have already found the slope in the previous step, which is 25. The slope represents the rate of change of distance with respect to time. Therefore, the car is traveling at a speed of 25 miles per hour.
For the third question, we need to find the distance from home after 3 hours and 15 minutes. To do this, we can substitute the value of x = 3.25 into the equation y = 25x + 15:
y = 25 * 3.25 + 15
y = 81.25 + 15
y = 96.25.
Therefore, the individual was approximately 96.25 miles from home after 3 hours and 15 minutes.
I hope this helps! Let me know if you have any further questions.