Question

write the equation of the line that passes through the points (3, 1) and (-2, 6).

Explanation:

Step1: Calculate the slope

The slope \( m \) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by \( m=\frac{y_2 - y_1}{x_2 - x_1} \). For the points \((3, 1)\) and \((-2, 6)\), we have \( x_1 = 3\), \( y_1 = 1\), \( x_2=-2\), \( y_2 = 6 \). So \( m=\frac{6 - 1}{-2 - 3}=\frac{5}{-5}=-1 \).

Step2: Use point - slope form

The point - slope form of a line is \( y - y_1=m(x - x_1) \). Let's use the point \((3, 1)\) and \( m=-1 \). Substituting these values, we get \( y - 1=-1(x - 3) \).

Step3: Simplify the equation

Expand the right - hand side: \( y - 1=-x + 3 \). Then add 1 to both sides to get the slope - intercept form \( y=-x+4 \). We can also write it in standard form \( x + y=4 \).

Answer:

The equation of the line is \( y=-x + 4 \) (or \( x + y=4 \))