hw to find the slope of a line simple

Answer 1

To find the slope of a line, you can use the formula:

\[ \text{slope} (m) = \frac{y_2 - y_1}{x_2 - x_1} \]

where \((x_1, y_1)\) and \((x_2, y_2)\) are two points on the line.

Steps to Find the Slope:

1. Identify Two Points on the Line: For example, let's use the points \((x_1, y_1)\) and \((x_2, y_2)\).

2. Subtract the y-coordinates: Calculate \(y_2 - y_1\).

3. Subtract the x-coordinates: Calculate \(x_2 - x_1\).

4. Divide the Differences: Divide the result from step 2 by the result from step 3 to find the slope \(m\).

Example:

Let’s find the slope of the line that passes through the points \((1, 2)\) and \((3, 4)\):

1. Identify the points: \((x_1, y_1) = (1, 2)\) and \((x_2, y_2) = (3, 4)\).

2. Calculate \(y_2 - y_1\): \[ 4 - 2 = 2 \]

3. Calculate \(x_2 - x_1\): \[ 3 - 1 = 2 \]

4. Divide the differences: \[ m = \frac{2}{2} = 1 \]

So, the slope of the line is \(1\).

Answer 2

i dont understand all the rest of the symbles

Answer 3

No problem! Let's simplify it by explaining the concepts without heavy symbols.

What is the Slope?

The slope of a line measures how steep it is. It tells you how much the line rises (goes up) or falls (goes down) as you move from left to right.

Steps to Find the Slope:

1. Pick Two Points on the Line: You need two points. For example, let's say we have two points:

   • Point A: (1, 2)
   • Point B: (3, 4)

   Here, the first number in each point is the "x" value (how far left or right), and the second number is the "y" value (how far up or down).

2. Find the Difference in Y (Up and Down):

   • Take the y-value of point B (which is 4) and subtract the y-value of point A (which is 2):

     4 - 2 = 2

   This tells you how much you go up or down when moving from point A to point B. In this case, you go up by 2.

3. Find the Difference in X (Left and Right):

   • Take the x-value of point B (which is 3) and subtract the x-value of point A (which is 1):

     3 - 1 = 2

   This tells you how much you go left or right when moving from point A to point B. In this case, you go right by 2.

4. Calculate the Slope:

   • Now, divide the difference in Y by the difference in X:

     2 (how much you went up) ÷ 2 (how much you went right) = 1

Conclusion:

The slope is 1. This means that for every 1 unit you go to the right, the line goes up 1 unit.

Visualize It:

If you draw a graph with these points, you’ll see that the line rises at a 45-degree angle, indicating a slope of 1.

If you have any specific part of this that you’d like me to clarify, just let me know!