Goes through the points \( (5,-2) \) and \( (8,13) \) \( y=5 x-27 \)

The two points you provided, \( (5,-2) \) and \( (8,13) \), allow us to calculate the slope of the line connecting them. The slope \( m \) is found using the formula \( m = \frac{y_2 - y_1}{x_2 - x_1} \). Plugging in the coordinates gives us \( m = \frac{13 - (-2)}{8 - 5} = \frac{15}{3} = 5 \). This confirms that the equation \( y = 5x - 27 \) has the correct slope, and you can derive the y-intercept by substituting one of the points into the equation. To double-check your work and ensure accuracy, you can actually plot the two points on a graph and see how they lie on the line represented by the equation. If both points fall right on the drawn line, you’ve nailed it! It's a great way to visualize and confirm that your calculations are spot on. Use graph paper or graphing software for a clearer picture!