Question

what is an equation of the line that passes through the points (6, -2) and (-1, 5)?

Explanation:

Step1: Calculate the slope

The slope \( m \) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by \( m=\frac{y_2 - y_1}{x_2 - x_1} \). Let \((x_1, y_1)=(6, - 2)\) and \((x_2, y_2)=(-1, 5)\). Then \( m=\frac{5-(-2)}{-1 - 6}=\frac{5 + 2}{-7}=\frac{7}{-7}=-1 \).

Step2: Use point - slope form

The point - slope form of a line is \( y - y_1=m(x - x_1) \). We can use the point \((6,-2)\) and \( m=-1 \). Substitute into the formula: \( y-(-2)=-1(x - 6) \), which simplifies to \( y + 2=-x + 6 \).

Step3: Convert to slope - intercept form

Subtract 2 from both sides of the equation \( y+2=-x + 6 \) to get \( y=-x+4 \). We can also write it in standard form \( x + y=4 \).

Answer:

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