Tutorial Exercise Find an equation of the line passing through the pair of points. Sketch the line. \[ (5,4),(-5,-5) \] Step 1 Compute the slope of the line. \( \square \)

To find the equation of the line passing through the points \((5, 4)\) and \((-5, -5)\), we will first compute the slope of the line. ### Step 1: Compute the slope of the line The formula for the slope \(m\) of a line passing through two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by: \[ m = \frac{y_2 - y_1}{x_2 - x_1} \] Here, we can assign: - \((x_1, y_1) = (5, 4)\) - \((x_2, y_2) = (-5, -5)\) Now, substituting these values into the slope formula: \[ m = \frac{-5 - 4}{-5 - 5} \] Calculating the numerator and denominator: \[ m = \frac{-9}{-10} = \frac{9}{10} \] So, the slope of the line is \(m = \frac{9}{10}\). ### Step 2: Find the equation of the line We can use the point-slope form of the equation of a line, which is: \[ y - y_1 = m(x - x_1) \] Using the point \((5, 4)\) and the slope \(m = \frac{9}{10}\): \[ y - 4 = \frac{9}{10}(x - 5) \] Now, we can simplify this equation to the slope-intercept form \(y = mx + b\). ### Step 3: Simplify the equation Distributing the slope on the right side: \[ y - 4 = \frac{9}{10}x - \frac{9}{10} \cdot 5 \] Calculating \(-\frac{9}{10} \cdot 5\): \[ -\frac{9}{10} \cdot 5 = -\frac{45}{10} = -4.5 \] Now, substituting this back into the equation: \[ y - 4 = \frac{9}{10}x - 4.5 \] Adding 4 to both sides: \[ y = \frac{9}{10}x - 4.5 + 4 \] Calculating \(-4.5 + 4\): \[ -4.5 + 4 = -0.5 \] Thus, the equation of the line is: \[ y = \frac{9}{10}x - 0.5 \] ### Step 4: Sketch the line To sketch the line, we can plot the two points \((5, 4)\) and \((-5, -5)\) and draw a line through them. The slope indicates that for every 10 units moved horizontally to the right, the line rises 9 units vertically. Now, let's summarize the findings: - Slope \(m = \frac{9}{10}\) - Equation of the line: \(y = \frac{9}{10}x - 0.5\) If you would like me to plot the line, please let me know!