Find an equation of the line that contains the given pair of points. \[ (-6,3),(-4,-3) \] The equation of the line is \( \square \) (Simplify your answer Type your answer in slope-intercept form. Type an inleger or a fraction for tho coelficiont and conslant.)

To find the equation of the line that passes through the points \((-6, 3)\) and \((-4, -3)\), we first need to calculate the slope (m) using the formula: \[ m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{-3 - 3}{-4 - (-6)} = \frac{-6}{2} = -3 \] Now, we can use the point-slope form of the line equation, \(y - y_1 = m(x - x_1)\). Let's use point \((-6, 3)\): \[ y - 3 = -3(x + 6) \] Expanding this, we get: \[ y - 3 = -3x - 18 \] Then, adding 3 to both sides yields: \[ y = -3x - 15 \] So the equation of the line in slope-intercept form is: \[ \boxed{y = -3x - 15} \] The equation of the line is \(y = -3x - 15\). To confirm, we can plug in the original points to ensure they satisfy the equation—both should yield true statements when substituted back into the equation. Wouldn't it be exciting if every math problem fit together like this puzzle? Every time you sketch a line, remember that behind every equation lies the story of the points that helped define it. With a little practice, you'll be able to master finding lines with ease!