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

To find the equation of the line that passes 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 the points, we get \( m = \frac{3 - (-4)}{-4 - 3} = \frac{7}{-7} = -1 \). Now, using point-slope form \( y - y_1 = m(x - x_1) \), we can substitute \( (3, -4) \) to get \( y + 4 = -1(x - 3) \). Simplifying gives the equation \( y = -x + 1 \). Now you have a cool line with a negative slope, going down to the right! Equations like these pop up all over the place—whether you're figuring out how to build a ramp or plotting paths in video games, knowing how to derive equations from points is super useful. Another fun fact: The two points you picked create a line that has special symmetry! If you were to reflect either point over the line \( y = x \), you'd land on the other point. It’s like they’re dancing across the diagonal! Being able to spot patterns like these can help you simplify problems and make calculations easier. Enjoy your exploration of lines and slopes!