To find the equation of a straight line passing through the point (3, 3) that is perpendicular to the line y = -3x - 4, you can follow these steps:
1. Determine the slope of the given line y = -3x - 4. In this case, the slope is -3 because the coefficient of x is -3 in the equation y = -3x - 4.
2. Since the line we want to find is perpendicular to the given line, the slope of the perpendicular line will be the negative reciprocal of the slope of the given line. So, the slope of the perpendicular line will be 1/3.
3. Use the point-slope form of the equation of a line, which is y - y1 = m(x - x1), where (x1, y1) is the given point (3, 3) and m is the slope of the line (1/3) to write the equation of the line.
4. Substitute the values of x1, y1, and m into the point-slope form equation to find the equation of the perpendicular line passing through (3, 3).
5. After substituting the values, simplify the equation to put it in the slope-intercept form y = mx + b, where m is the slope and b is the y-intercept.
By following these steps, you will be able to find the equation of the straight line passing through the point (3, 3) that is perpendicular to the given line y = -3x - 4.
