Question What is an equation of the line that passes through the points \( (3,-4) \) and \( (-4,3) \) ? Answer Attempt 1 out of 3 Submit Answer

To find the equation of the line passing through the points \( (3,-4) \) and \( (-4,3) \), we first calculate the slope \( m \) using the formula \( m = \frac{y_2 - y_1}{x_2 - x_1} \). Plugging in our points, we get \( m = \frac{3 - (-4)}{-4 - 3} = \frac{3 + 4}{-4 - 3} = \frac{7}{-7} = -1 \). Now, using the point-slope form \( y - y_1 = m(x - x_1) \), we can choose one of the points, say \( (3, -4) \). Substituting, we get \( y - (-4) = -1(x - 3) \), simplifying to \( y + 4 = -x + 3 \). Finally, rearranging gives us the equation of the line: \( y = -x - 1 \). Additionally, did you know that the concept of a line in geometry dates back to ancient civilizations? The Greeks and Egyptians explored the properties of lines, leading to significant advancements in mathematics and geometry! Also, if you're ever faced with writing an equation from given coordinates, remember to double-check your slope and that the formula is used correctly. It’s easy to miscalculate if you rush!