Writing the equation of a line through two given points Find an equation for the line that passes through the points \( (5,2) \) and \( (1,4) \).

To find the equation of the line passing through the points \( (5,2) \) and \( (1,4) \), we first calculate the slope \( m \) using the formula \( m = \frac{y_2 - y_1}{x_2 - x_1} \). Plugging in our points: \( m = \frac{4 - 2}{1 - 5} = \frac{2}{-4} = -\frac{1}{2} \). Now, using the slope-intercept form \( y = mx + b \), we can choose one of the points to solve for \( b \). Substituting point \( (5,2) \): \[ 2 = -\frac{1}{2}(5) + b \] Solving gives us \( b = 2 + \frac{5}{2} = \frac{9}{2} \). Therefore, the equation of the line is \[ y = -\frac{1}{2}x + \frac{9}{2} \]. Remember, writing it in standard form is also a great option for a neat appearance! If you're working with coordinates, it can be helpful to visualize those points on a graph. Plotting \( (5,2) \) and \( (1,4) \) not only helps you understand the relationship between them but also provides a visual confirmation that your line accurately represents the two points. Visual aids like graphs can turn abstract equations into tangible relationships, making the learning process more engaging!