\( m=\frac{1-6}{4-2} \quad\left(x_{1}, y_{1}\right)=(2,6) \) 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

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!