$$ m=\frac{1-6}{4-2} \quad\left(x_{1}, y_{1}\right)=(2,6) $$ and $$ \left(x_{2}, y_{2}\right)=(4,1) $$ $$ m=\frac{\square}{\square} $$ or $$ -2.5 \quad $$ Simplify. Step 2 Determine the $$ y $$-intercept and write the equation. The $$ v $$-intercent ic ahnit 11 heraıco the line anopars to cros

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Sure, let's work through the problem step by step to find the equation of the line passing through the points $$(2, 6)$$ and $$(4, 1)$$.

### **Step 1: Calculate the Slope ($$m$$)**

The slope of a line ($$m$$) passing through two points $$\left(x_1, y_1\right)$$ and $$\left(x_2, y_2\right)$$ is given by the formula:

$$
m = \frac{y_2 - y_1}{x_2 - x_1}
$$

Plugging in the given points $$(2, 6)$$ and $$(4, 1)$$:

$$
m = \frac{1 - 6}{4 - 2} = \frac{-5}{2} = -2.5
$$

So, the slope $$m$$ is **$$-2.5$$**.

### **Step 2: Determine the $$y$$-Intercept ($$b$$)**

The equation of a straight line in slope-intercept form is:

$$
y = mx + b
$$

We already know $$m = -2.5$$, so the equation becomes:

$$
y = -2.5x + b
$$

To find $$b$$, substitute the coordinates of one of the given points into the equation. Let's use the point $$(2, 6)$$:

$$
6 = -2.5(2) + b
$$

$$
6 = -5 + b
$$

$$
b = 6 + 5 = 11
$$

So, the $$y$$-intercept $$b$$ is **$$11$$**.

### **Step 3: Write the Final Equation**

Now that we have both the slope and the $$y$$-intercept, we can write the equation of the line:

$$
y = -2.5x + 11
$$

### **Summary**

- **Slope ($$m$$)**: $$-2.5$$
- **$$y$$-Intercept ($$b$$)**: $$11$$
- **Equation of the Line**: $$y = -2.5x + 11$$

### **Graphical Interpretation**

The $$y$$-intercept ($$b = 11$$) is the point where the line crosses the $$y$$-axis. This means when $$x = 0$$, $$y = 11$$. Plotting this point along with the slope will allow you to draw the line accurately on a graph.

If you need further assistance or have any more questions, feel free to ask!
The slope $$ m $$ is $$-2.5$$, and the $$ y $$-intercept is $$11$$. The equation of the line is $$ y = -2.5x + 11 $$.

and
or Simplify.
Step 2 Determine the -intercept and write the equation.
The -intercent ic ahnit 11 heraıco the line anopars to cros

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and or Simplify. Step 2 Determine the -intercept and write the equation. The -intercent ic ahnit 11 heraıco the line anopars to cros