What is the equation (in slope-intercept form) of the line passing through the points (6, 1) and (0, 4)?
y=-1/2x+2
y=-1/2+ 11/2
y=-2x+4
y=-2x+8
Suppose that the daily cost and revenue functions for the production and sale of x stopwatches are given by C(x) = 6x + 160 and R(x) = 10x where C(x) and R(x) are in dollars.
How many watches would need to be produced and sold each day in order to break even?
10
16
80/3
40
first find the slope ....
in your case that would be (4-1)/(0-6) = 3/-6 = -1/2
so that eliminates the last two choices.
try subbing (6,1) into the other two.
It does not satisfy either one, so there is something wrong with your answers.
should be :
let the equation be y = (-1/2)x + b
sub in (6,1)
1 = (-1/2)(6) + b
b = 4
the equation should be
y = (-1/2)x + 4
(notice the second point satisfies my equation)
for the second question,
set 10x = 6x + 160 and solve for x, real easy !
To find the equation of a line passing through two given points, we can use the slope-intercept form of a linear equation, which is y = mx + b, where m represents the slope and b represents the y-intercept.
1) Finding the slope (m):
The slope of a line passing through two points (x1, y1) and (x2, y2) is given by the formula:
m = (y2 - y1) / (x2 - x1)
Using the given points (6, 1) and (0, 4), we can find the slope:
m = (4 - 1) / (0 - 6) = 3 / -6 = -1/2
2) Finding the y-intercept (b):
Now, we have the slope (m = -1/2) and a point (6, 1). We can substitute these values into the slope-intercept form (y = mx + b) and solve for b:
1 = (-1/2)(6) + b
1 = -3 + b
b = 4
3) Writing the equation in slope-intercept form:
Now that we have the slope (m = -1/2) and y-intercept (b = 4), we can write the equation of the line:
y = -1/2x + 4
Therefore, the correct equation (in slope-intercept form) of the line passing through the points (6, 1) and (0, 4) is y = -1/2x + 4.
As for the second question, to find the number of watches that need to be produced and sold each day in order to break even, we need to set the cost function (C(x)) equal to the revenue function (R(x)) and solve for x.
Given:
C(x) = 6x + 160
R(x) = 10x
Setting C(x) = R(x), we have:
6x + 160 = 10x
Simplifying the equation, we can subtract 6x from both sides:
160 = 4x
Now, dividing both sides by 4, we get:
40 = x
Therefore, in order to break even, 40 watches would need to be produced and sold each day.