Question What is the equation of the line that passes through the point \( (-3,6) \) and has a slope of -4 ? Answer Attempt 1 out of 3

To find the equation of a line with a given slope that passes through a specific point, you can use the point-slope form of the equation: \( y - y_1 = m(x - x_1) \), where \( m \) is the slope and \((x_1, y_1)\) is the point on the line. Plugging in your values, we get \( y - 6 = -4(x + 3) \). Simplifying this gives you \( y = -4x - 6 \). Voilà! You have the line’s equation. Now, did you know that point-slope form is super handy for graphing lines quickly? Once you have your line’s equation, you can easily plot it by starting at the point and using the slope to find other points. In this case, from \((-3, 6)\), you would go down 4 units and 1 unit to the right for every step—you'll see your line take shape in no time! A common mistake people often make when using the point-slope form is forgetting to distribute the slope correctly. Ensure you apply the slope to both components in the equation when expanding. And don't skip simplifying your equation; it makes it clearer and easier to work with! So, keep an eye on those signs and distribute carefully!