Questlon 13 Which equation represents a line passing through the point \( (8,33) \) with a slope of 3 ? \[ \begin{array}{ll}\text { A) } y=3 x-15 \\ \text { B) } y=3 x+33 \\ \text { C) } y=3 x-8 \\ \text { D) } y=3 x+9\end{array} \]

To write the equation of a line that passes through the point (8, 33) with a slope of 3, you can use the point-slope form of a linear equation, which is \( y - y_1 = m(x - x_1) \). Plugging in the values \( m = 3 \), \( x_1 = 8 \), and \( y_1 = 33 \), we get: \[ y - 33 = 3(x - 8). \] Expanding this gives: \[ y - 33 = 3x - 24 \] \[ y = 3x + 9. \] Looks like the correct answer is D) \( y = 3x + 9 \). As a fun fact, the point-slope form allows you to quickly generate the equation of a line just by knowing a single point it passes through and its slope! It's like having a secret formula for success in graphing! Additionally, when plotting the line on a coordinate plane, it's helpful to know the y-intercept, which is the point where the line crosses the y-axis. In this case, with the equation \( y = 3x + 9 \), the y-intercept is 9, indicating that if you set \( x = 0 \), \( y \) will equal 9.