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!!!
a marble is selected at random from a jar containing 6 red marbles,4 yellow marbles, 2 green marbles. what is the probability of getting a red marble
To find the slope-intercept form of the line, we need to calculate the slope (m) and the y-intercept (b).
Step 1: Calculate the slope (m):
The slope of a line can be found using the formula: m = (y2 - y1) / (x2 - x1)
Given the points (1, 40) and (3, 90), we can substitute the values into the formula:
m = (90 - 40) / (3 - 1)
m = 50 / 2
m = 25
Step 2: Calculate the y-intercept (b):
To calculate the y-intercept, we can choose any point on the line and substitute its coordinates into the slope-intercept form (y = mx + b) to solve for b.
Using the point (1, 40):
40 = 25(1) + b
40 = 25 + b
b = 40 - 25
b = 15
Therefore, the slope-intercept form of the line is: y = 25x + 15.
To determine how fast the car is traveling, we need to use the slope of the line, which represents the rate of change of the distance with respect to time.
The slope of 25 indicates that for every hour that passes, the distance from home increases by 25 miles. Therefore, the car is traveling at a speed of 25 miles per hour.
To calculate how far the individual was from home initially (at x = 0), we can substitute x = 0 into the equation y = 25x + 15:
y = 25(0) + 15
y = 15
Therefore, the individual was initially 15 miles from home.
To find how far the individual was from home after 3 hours and 15 minutes (x = 3.25), we can substitute 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 96.25 miles from home after 3 hours and 15 minutes.
To find the slope-intercept form of the line, we can use the formula:
y = mx + b
Where "m" represents the slope and "b" represents the y-intercept.
1. Find the slope (m):
The slope of a line can be found using the formula:
m = (y2 - y1) / (x2 - x1)
Using the given points (1, 40) and (3, 90):
m = (90 - 40) / (3 - 1)
m = 50 / 2
m = 25
2. Find the y-intercept (b):
To find the y-intercept, we can substitute one of the points into the slope-intercept form equation (y = mx + b):
40 = 25(1) + b
40 = 25 + b
b = 40 - 25
b = 15
Therefore, the slope-intercept form of the line is:
y = 25x + 15
To find how fast the car is traveling, we can use the slope of the line since the slope represents the rate of change or speed.
The car is traveling at a speed of __25__ miles per hour.
To find the initial distance from home, we can substitute x = 0 into the equation:
y = 25(0) + 15
y = 15
Therefore, the individual was initially __15__ miles away from home.
To find the distance from home after 3 hours and 15 minutes, we substitute x = 3.25 into the equation:
y = 25(3.25) + 15
y = 81.25 + 15
y = 96.25
Therefore, the individual was __96.25__ miles away from home after 3 hours and 15 minutes.