Question

question
what is an equation of the line that passes through the points (6, -7) and (4, -6)?

Explanation:

Step1: Find 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, \( (x_1,y_1)=(6, - 7) \) and \( (x_2,y_2)=(4,-6) \). So \( m=\frac{-6-(-7)}{4 - 6}=\frac{-6 + 7}{-2}=\frac{1}{-2}=-\frac{1}{2} \).

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 \( (6,-7) \). Substitute \( m =-\frac{1}{2} \), \( x_1 = 6 \) and \( y_1=-7 \) into the formula:
\( y-(-7)=-\frac{1}{2}(x - 6) \)
\( y + 7=-\frac{1}{2}x+3 \)

Step3: Convert to slope - intercept form

Subtract 7 from both sides: \( y=-\frac{1}{2}x+3 - 7 \), so \( y=-\frac{1}{2}x-4 \)

Answer:

\( y =-\frac{1}{2}x - 4 \) (or in standard form \( x+2y=-8 \))