Question

Without calculating, state whether the slope of the line through the points is positive, negative, zero, or undefined. (6,1),(3,1)

Short answer

The slope of the line through points (6,1) and (3,1) is zero.

Step-by-step solution

Identify the coordinates

The first coordinate is (6,1) and the second is (3,1). The coordinates are given in the form (x,y). Thus, for the first point, x1=6 and y1=1. For the second point, x2=3 and y2=1.

Apply the formula for slope

The slope m of a line through points (x1,y1) and (x2,y2) is calculated as m = (y2-y1)/(x2-x1). Substituting the given values into the formula, we get m = (1-1)/(3-6).

Simplify the expression

Simplify the numerator and the denominator separately. Here, the numerator (y2-y1) equals 0 because 1 minus 1 is 0. The denominator (x2-x1) equals -3 because 3 minus 6 is -3.

Conclude the type of the slope

As the numerator (vertical change) is zero and the denominator (horizontal change) is not zero, the slope of the line is zero which implies the line is horizontal.