Fragen 24
Antworten 56


Use Desmos to graph the points. 

Find the slope of the line. Because the slope is positive, and we're trying to find what point intersects with the y-axis, we're going to start from point (3, 11) and end at point (1, 7).


To get from (3, 11) to (1, 7), go down 4, and to the left 2. (or left 2, and down 4 - doesn't matter which way you do it!!)


Using the slope, find your next point going down 4 and to the left 2 of (1, 7).

Your next point should be (-1, 3). 


Your y-axis is the line that is vertical, so find the point at which the line you plotted intersects this axis. In this case, an easy way of calculating the intersection would be to find the point between (1, 7) and (-1, 3).

The intersection is (0, 5).


Use Desmos to graph each equation, and then count each intersection.


You'll find they intersect at (0,0), (-1.562, -3.808), and (2.562, 16.808).


There are 3 intersections.


To solve this problem, I went to Youtube. If you want to follow along and do it, here's the link to the video I used, but if you want an explanation without watching a video, I will do my best to explain below. 


Plot the points given. I labeled them KL in the graph below.




As you can see, I have made a lot of side notes. It may be hard to understand at first, but bare with me.

I drew a straight line across from K, and then a straight line down from L, connecting the both into a triangle.


The point I labeled at (?,?) is the point we're trying to find. It's only an APPROXIMATE spot!!!! This is just a visual for your understanding.

To divide the segment into the 5:3 ratio, we must conclude that there's some point that divides x into the ratio 5:3 and there's some point that divides y into the ratio 5:3. (I represented this by putting 5x and 3x, and 5y and 3y.)


Then, we need to think about what the total change in x is from point K (-4, -3) to point L (5, 3). Doing this, we find the distance between the x on each point. So ask yourself what the distance is from -4 to 5.
It is going to be 9. (I represented this on the image, where delta = 9)


Next, we do the same for the distance between y on each point. Ask yourself what the distance is from -3 to 3.
It's going to be 6. (I also represented this on the image too, where delta = 6.)




Now that you understand everything on the graph, you can use the information given to find the point that divides the segment from each point.

Form two equations with x and y from the graph, and then solve. This is not the last step yet, sadly. 


5x + 3x = 9 

8x = 9

x = 9/8


3y + 5y = 6

8y = 6

y = 6/8

y = 3/4


Using the point (-4, -3), we can use the x and y values to finally determine the point that divides the segment from each point.


Let's label (?,?) as P. 


P ( -4 + (5 x (9/8)), -3 + (5 x (3/4)) )

Solve for for point P.


P ( -4 + (5 x (9/8)), -3 + (5 x (3/4)) )

P ( -4 + 5.525, -3 + 3.75 )

P ( 1.625, 0.75 ) 
OR you can flip it into a fraction.

P ( 13/8 , 3/4 )


The point that divides the segment from each point can be represented at ( 13/8 , 3/4 ).


I used to graph the equations.


The equations intersect at (1,1) and (0,0). So they intersect twice.