A boat is worth $7,000 when it is 5 years old and $2,000 when it is 10 years old. What is the slope intercept equation?
You have two points: (5,7000) and (10,2000)
the two-point equation for the line is thus
(y-7000)/(x-5) = (2000-7000)/(10-5)
or, after rearranging things a bit:
y = -1000x + 12000
That is, the value started at $12,000, and depreciates $1000/year
Well, if we consider the boat's age (x) as the independent variable and the boat's worth (y) as the dependent variable, we can use the slope-intercept equation: y = mx + b. So, let's find the slope (m) and y-intercept (b).
We'll designate the boat's age at 5 years as x1, and its worth at that age as y1 ($7,000). Similarly, we'll designate the boat's age at 10 years as x2 and its worth at that age as y2 ($2,000).
Now, let's calculate the slope (m):
m = (y2 - y1) / (x2 - x1)
= ($2,000 - $7,000) / (10 - 5)
= (-$5,000) / 5
= -$1,000
So, the slope (m) is -1,000.
Now, let's find the y-intercept (b) using the point-slope form: y - y1 = m(x - x1).
Using (x1, y1) = (5, $7,000) and m = -1,000, we have:
y - $7,000 = -1,000(x - 5)
y - $7,000 = -1,000x + 5,000
y = -1,000x + $5,000 + $7,000
y = -1,000x + $12,000
So, the slope-intercept equation for the boat's worth (y) in terms of its age (x) is y = -1,000x + $12,000.
To find the slope-intercept equation, we need to determine the equation of a straight line using two points: (5, 7000) and (10, 2000).
Let's first find the slope (m) using the formula:
m = (y2 - y1) / (x2 - x1)
Substituting the given values:
m = (2000 - 7000) / (10 - 5)
m = -5000 / 5
m = -1000
Now that we have the slope, let's use the slope-intercept form of a line:
y = mx + b
where m is the slope and b is the y-intercept.
Substituting the slope (-1000) and the coordinates of one point (5, 7000):
7000 = -1000(5) + b
7000 = -5000 + b
b = 7000 + 5000
b = 12000
Therefore, the slope-intercept equation for the boat's value can be written as:
y = -1000x + 12000
To find the slope-intercept equation, we need to determine the relationship between the age of the boat and its value.
The slope-intercept equation has the form: y = mx + b.
where y represents the value, x represents the age, m represents the slope, and b represents the y-intercept.
First, let's determine the slope (m) using the given data. The slope is calculated by finding the change in y divided by the change in x. In this case, y represents the value and x represents the age.
Change in value = $2,000 - $7,000 = -$5,000
Change in age = 10 years - 5 years = 5 years
Now we can calculate the slope:
slope (m) = change in value / change in age
= -$5,000 / 5 years
= -$1,000 per year
Next, we need to find the y-intercept (b) which is the value of y when x is 0. In this case, it would be the value of the boat when it is newly purchased (0 years old). However, this information is not provided. To proceed, we will assume that the boat has a value of $7,000 when it is newly purchased (0 years old).
Now let's substitute the values into the equation:
y = mx + b
y = -$1,000x + $7,000
Therefore, the slope-intercept equation for the value (y) of the boat as a function of age (x) is:
y = -$1,000x + $7,000