Question 84511: Could I possibly get some help on these questions. Whatever help I can get I would appreciate it.
Find the slope of the line passing through the points (4,0) and (4,5)
Find the slope passing through the points (-9,-4) and (0,-4).
Determine which two equations represent parallel lines.
a. y=5/3x+4 b. y=-3/5x-7 c. y=2x+8 d. y=2x-4.
I was thinking c and d would be parallel, but I would like to get that verified before I turn that in.
Write the equation of the line with slope -2 and y-intercept (0,0). Then graph the line.
Answer by jim_thompson5910(21667)   (Show Source):
You can put this solution on YOUR website!
| Solved by pluggable solver: Finding the slope |
To find the slope going from (4,0) to (4,5) we are going to calculate the change in y over the change in x, or the rise over the run. The change is the difference between the two coordinates. So if the y-coordinate of a point goes from 0 to 5, the change in these numbers is 5 (since  ). If the x-coordinate changes from 4 to 4, then the change is 0 (since  ). So to calculate the slope we use this formula:
Slope:
 where m is the slope
So now we let  , , , Now plug these numbers into the slope formula:
 Since the two points have the same x-coordinate, we have a denominator of zero. Remember we cannot divide by zero. In other words, this is not possible:  (we cannot divide any number by 0) This means the slope is undefined, and because we don't have any change in x, we have a vertical line at x=4 |
| Solved by pluggable solver: Finding the slope |
To find the slope going from (-9,-4) to (0,-4) we are going to calculate the change in y over the change in x, or the rise over the run. The change is the difference between the two coordinates. So if the y-coordinate of a point goes from -4 to -4, the change in these numbers is 0 (since  ). If the x-coordinate changes from -9 to 0, then the change is 9 (since  ). So to calculate the slope we use this formula:
Slope:
where m is the slope
So now we let  , , , Now plug these numbers into the slope formula:
So after simplification the slope is  |
Any two parallel lines have equal slopes. Since c) and d) have equal slopes of 2, this means they are parallel.
| Solved by pluggable solver: FIND a line by slope and one point |
What we know about the line whose equation we are trying to find out:
- it goes through point (0, 0)
- it has a slope of -2
First, let's draw a diagram of the coordinate system with point (0, 0) plotted with a little blue dot:
Write this down: the formula for the equation, given point  and intercept a, is
 (see a paragraph below explaining why this formula is correct)
Given that a=-2, and  , we have the equation of the line:
Explanation: Why did we use formula  ? Explanation goes here. We are trying to find equation y=ax+b. The value of slope (a) is already given to us. We need to find b. If a point ( ,  ) lies on the line, it means that it satisfies the equation of the line. So, our equation holds for (, ):  Here, we know a, , and , and do not know b. It is easy to find out:  . So, then, the equation of the line is:  .
Here's the graph:
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