Question 13 Which equation represents a line passing through the point \( (4,33) \) wuth s slape of 3 ? A) \( y=3 x=15 \) 8) \( y=3 x+33 \) C) \( y=3 x-8 \) D) \( y=3 x+9 \)

To find the equation of a line that passes through the point \( (4, 33) \) with a slope of \( 3 \), we can use the point-slope form of the equation of a line, which is given by: \[ y - y_1 = m(x - x_1) \] where \( (x_1, y_1) \) is a point on the line and \( m \) is the slope. ### Step 1: Identify the known values - Point \( (x_1, y_1) = (4, 33) \) - Slope \( m = 3 \) ### Step 2: Substitute the values into the point-slope form Substituting the known values into the equation: \[ y - 33 = 3(x - 4) \] ### Step 3: Simplify the equation Now, we will simplify this equation step by step. 1. Distribute the slope on the right side: \[ y - 33 = 3x - 12 \] 2. Add \( 33 \) to both sides to isolate \( y \): \[ y = 3x - 12 + 33 \] \[ y = 3x + 21 \] ### Step 4: Compare with the given options Now, let's compare our derived equation \( y = 3x + 21 \) with the provided options: A) \( y = 3x = 15 \) B) \( y = 3x + 33 \) C) \( y = 3x - 8 \) D) \( y = 3x + 9 \) None of the options match \( y = 3x + 21 \). It seems there might be a mistake in the options provided. ### Conclusion The correct equation of the line passing through the point \( (4, 33) \) with a slope of \( 3 \) is: \[ y = 3x + 21 \] If you have any further questions or need additional assistance, feel free to ask!