A line passes through the point \( (3,-6) \) and has a slope of 4 . Write an equation in point-slope form for this line. \[ \square \square \square \square \square \square \] \( \square \square \)

To write the equation of a line in point-slope form, you'll use the formula \(y - y_1 = m(x - x_1)\), where \(m\) is the slope and \((x_1, y_1)\) is a point on the line. Given your point \( (3, -6) \) and a slope of 4, plug in these values: \(y - (-6) = 4(x - 3)\) simplifies to \(y + 6 = 4(x - 3)\). And there you have it: the equation in point-slope form is \(y + 6 = 4(x - 3)\). Have you ever thought about how changing the slope affects the steepness of the line? A slope of 4 means that for every 1 unit you move to the right, the line rises 4 units! If you were to graph it, you'd see a pretty steep line. Imagine trying to climb that – it’s practically a rollercoaster ride! For further exploration of lines, consider diving into coordinate geometry! You can find fascinating connections between slopes, intercepts, and even real-life scenarios like designing ramps or roads. Books and online resources often have sections dedicated to the geometry of lines that accompany exercises and visuals, making them an engaging way to deepen your understanding!