Question

goes through points (5,6) and (2, 15)

1. $y = 3x + 21$
2. $y = -3x - 9$
3. $y = 3x - 9$
4. $y = -3x + 21$

Explanation:

Step1: Calculate the slope

The slope \( m \) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by \( m=\frac{y_2 - y_1}{x_2 - x_1} \). Here, \((x_1,y_1)=(5,6)\) and \((x_2,y_2)=(2,15)\), so \( m=\frac{15 - 6}{2 - 5}=\frac{9}{-3}=- 3 \).

Step2: Use point - slope form

The point - slope form of a line is \( y - y_1=m(x - x_1) \). Using the point \((5,6)\) and \( m=-3 \), we have \( y - 6=-3(x - 5) \).

Step3: Simplify the equation

Expand the right - hand side: \( y - 6=-3x + 15 \). Then add 6 to both sides: \( y=-3x+15 + 6=-3x + 21 \).

Answer:

\( y = - 3x+21 \) (the blue - colored option with the equation \( y=-3x + 21 \))