Graph the lines by finding the points of intersection with the axes (intercepts):
1 answer:
The equation is in slope-intercept form, so you can read the equation to find the y-intercept is (0, -1).
Since the slope is -1/2, the graph goes <em>up</em> 1 unit for each 2 units to the <em>left</em>. The x-axis is up 1 unit from the y-intercept, so the x-intercept is 2 units to the left of x=0, at (-2, 0).
The graph is the line that goes through the points (0, -1) and (-2, 0).
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If you like, you can put the equation into intercept form, which shows you both the x- and y-intercepts at once. That form is ...
... x/a + y/b = 1
where <em>a</em> and <em>b</em> are the x- and y-intercepts.
If we add 1-y to the given equation, we have ...
... 1 = (-1/2)x - y
... 1 = x/(-2) + y/(-1) . . . . intercept form
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Answer:
P is exactly 3km east from the oil refinery.
Step-by-step explanation:
Let's d be the distance in km from the oil refinery to point P. So the horizontal distance from P to the storage is 3 - d and the vertical distance is 2. Hence the diagonal distance is:
So the cost of laying pipe under water with this distance is
And the cost of laying pipe over land from the refinery to point P is 400000d. Hence the total cost:
We can find the minimum value of this by taking the 1st derivative and set it to 0
We can move the first term over to the right hand side and divide both sides by 400000
From here we can square up both sides
d = 3
So the cost of pipeline is minimum when P is exactly 3km east from the oil refinery.