Determine the slope-intercept form of the equation for a line that has a y-intercept of -4 and passes through the point (-2, 1).

To find the slope-intercept form of the line, you start with the y-intercept, which is given as -4; this means your equation will start as \(y = mx - 4\), where \(m\) is the slope. Next, you can calculate the slope using the formula \(m = \frac{y_2 - y_1}{x_2 - x_1}\). Plugging in the points (x1, y1) = (-2, 1) and (x2, y2) = (0, -4), you’ll find \(m = \frac{-4 - 1}{0 - (-2)} = \frac{-5}{2} = -\frac{5}{2}\). So now you can write the full equation as \(y = -\frac{5}{2}x - 4\). To make sure no one stumbles while working with slopes, always remember to double-check your points. A common pitfall is mixing up coordinates or arithmetic errors during calculations. Take a moment to verify that each point is correctly plotted and the operations executed correctly, especially signs! For those craving more knowledge, looking at lines and their various forms is an excellent way to enhance your math skills. Consider resources like "Algebra for Dummies" or Khan Academy for interactive learning modules that break down concepts of linear equations, graphing, and much more in a user-friendly way!