point A (-2,3) lies on a line with a slope of 2. Describe how to find two points on the line on either side of A.
since the slope is 2, y changes by 2 whenever x changes by 1.
So, pick a point 1 unit to the right or left of (-2,3)
These would be (-3,?) and (4,?)
Since y changes by 2 for every 1 in x, the two points would be 2 units above or below (-2,3):
(-2,1) and (4,5)
You could have picked any other two x values, just make sure that the difference in y is twice the difference in x.
thank you Steve!
Point A(-2, 3) lies on a line with a slope of 2. Describe how to find two points on the line on either side of A
Well, finding two points on either side of point A (-2,3) with a given slope of 2 is like finding a sandwich with extra cheese. Let's take a cheesy approach to this math problem!
First, to find a point on the line right next to point A, we'll add a little cheese to the x-coordinate. Let's add 1. That would give us point B (-1,3). Now we have one tasty point!
Next, let's find a point on the line with a little more distance from point A. To do that, let's add more cheese to the x-coordinate. Let's add 2 this time. That would give us point C (0,3). Voila, another delicious point!
So, we've found two points, B (-1,3) and C (0,3), on either side of A (-2,3). And just like that, we've made a mathematically cheesy sandwich! Enjoy the flavor of those points!
To find two points on the line with a given slope that lie on either side of point A, you can follow these steps:
1. Start with the coordinates of point A, which are (-2, 3).
2. Determine the direction of the line based on the slope. In this case, the slope is positive (+2), indicating that the line is increasing as you move from left to right.
3. To find a point on the line to the right of point A, consider increasing the x-coordinate. Since the slope is 2, you can add 1 to the x-coordinate. Therefore, if you add 1 to the x-coordinate of point A (-2 + 1 = -1), you get the x-coordinate of the first point on the line to the right.
- The first point is (-1, y), where y is yet to be determined.
4. To find the corresponding y-coordinate for the first point on the line, multiply the change in x by the slope. In this case, the change in x is 1 and the slope is 2. Thus, the change in y is 1 * 2 = 2.
- The first point becomes (-1, 3 + 2) = (-1, 5).
5. Repeat the above steps to find a point on the line to the left of point A. Subtract 1 from the x-coordinate of point A: -2 - 1 = -3.
- The second point is (-3, y), where y is yet to be determined.
6. Find the corresponding y-coordinate for the second point on the line by multiplying the change in x (which is 1) by the slope (which is 2):
- The change in y is 1 * 2 = 2.
- The second point becomes (-3, 3 - 2) = (-3, 1).
Therefore, the two points on the line with a slope of 2, lying on either side of point A (-2, 3), are (-1, 5) and (-3, 1).