The following graph shows how a 4-color web printing press depreciates from the year 2006 to the year 2010. It was purchased new in the year 2006; therefore x = 0 represents the year 2006.
X – axis (horizontal) = years starting from 0 = 2006 and increasing by 0.5 years Y – axis (vertical) = price in $ amounts from 12,000 to 120,000
a) List the coordinates of any two points on the graph in (x, y) form. The numbers on the horizontal axis are 0.5, 1.0, 1.5, 2.0, 2.5, 3.0, 3.5, and 4.0.
(___, ___),(___, ___)
b) Find the slope of this line:
Answer:
Show your work here:
c) Find the linear equation of this line in slope-intercept form.
Answer:
Show what is the answer and how did you get it.
A line has a slope of 0.5 and a y-intercept of (0, -2). What is the value of y when x = 4?
a) To find the coordinates of two points on the graph, we need to look at the intersections between the graph and the horizontal axis.
Given the numbers on the horizontal axis as 0.5, 1.0, 1.5, 2.0, 2.5, 3.0, 3.5, and 4.0, we can read the corresponding values on the vertical axis.
Let's assume the first point is at x = 1.5. By looking at the graph, we can see that the corresponding y-value is approximately $90,000. Therefore, the first point is (1.5, 90,000).
For the second point, let's assume x = 3.0. By looking at the graph, we can see that the corresponding y-value is approximately $50,000. Therefore, the second point is (3.0, 50,000).
So, the coordinates of the two points are (1.5, 90,000) and (3.0, 50,000).
b) To find the slope of the line, we can use the formula:
slope = (change in y)/(change in x)
Let's choose the first point (1.5, 90,000) and the second point (3.0, 50,000).
Change in y = 50,000 - 90,000 = -40,000
Change in x = 3.0 - 1.5 = 1.5
slope = (-40,000)/(1.5) = -26,666.67
Therefore, the slope of the line is approximately -26,666.67.
c) To find the linear equation of the line in slope-intercept form (y = mx + b), we need to substitute the slope and the coordinates of either point into the equation and solve for b.
Using the first point (1.5, 90,000), we have:
90,000 = (-26,666.67)(1.5) + b
90,000 = -40,000 + b
Now, solve for b:
b = 90,000 - (-40,000)
b = 130,000
The linear equation of the line in slope-intercept form is:
y = -26,666.67x + 130,000
Therefore, the answer is y = -26,666.67x + 130,000.