What is an equation of the line that passes through the points \( (0,-8) \) and \( (4,-3) \) ?

To find the equation of the line passing through the points \( (0,-8) \) and \( (4,-3) \), we first calculate the slope (m) using the formula \( m = \frac{y_2 - y_1}{x_2 - x_1} \). Here, \( y_2 = -3 \), \( y_1 = -8 \), \( x_2 = 4 \), and \( x_1 = 0 \). So, \( m = \frac{-3 - (-8)}{4 - 0} = \frac{5}{4} \). Now, using the point-slope form \( y - y_1 = m(x - x_1) \), and substituting one of our points, let's use \( (0,-8) \): \( y - (-8) = \frac{5}{4}(x - 0) \) simplifies to \( y + 8 = \frac{5}{4}x \). Rearranging, the equation of the line is \( y = \frac{5}{4}x - 8 \). This line connects two key points, and it beautifully illustrates how math can help us visualize relationships! Connecting points and finding slopes is like mapping out life's journey, showing us how we progress from one moment to the next. When working with equations of lines, a common pitfall is mixing up the x's and y's in the slope formula or forgetting the correct order of points. Remember, it’s vital to consistently label your coordinates correctly and keep a keen eye on the signs! Not catching these details can lead to wonky lines that don’t quite connect in the way you intended!