What is an equation of the line that passes through the points \( (8,0) \) and \( (3,-5) \) ?

To find the equation of the line that passes through the points \( (8,0) \) and \( (3,-5) \), we first need to calculate the slope (m). The formula for the slope between two points \( (x_1, y_1) \) and \( (x_2, y_2) \) is given by: \[ m = \frac{y_2 - y_1}{x_2 - x_1} \] Substituting the points \( (8,0) \) and \( (3,-5) \): \[ m = \frac{-5 - 0}{3 - 8} = \frac{-5}{-5} = 1 \] Now that we have the slope, we can use the point-slope form of the line equation: \[ y - y_1 = m(x - x_1) \] Using the point \( (8,0) \) and the slope \( m = 1 \): \[ y - 0 = 1(x - 8) \] This simplifies to: \[ y = x - 8 \] And there you have it: the equation of the line is \( y = x - 8 \)! Now, speaking of our friends the Cartesian coordinates, did you know that the slope of a line can really shift your perspective? Imagine you're hiking up a hill (with a slope!). If it's too steep, you're going to need some energy bars! Keep that in mind the next time you’re trying to describe the steepness of a path. When graphing lines, it's important to use points that are easy to work with, like whole numbers or integers, especially if you're drawing by hand. One common mistake is trying to connect points with unclear calculations. Always double-check your slope and intercept math to avoid winding up on the wrong path!