Question

for each line, determine whether the slope is positive, negative, zero, or undefined. line 1 line 2 line 3 line 4 check

Explanation:

Line 1

• Vertical line:

A vertical line has an undefined slope. The formula for slope is \(m=\frac{y_2 - y_1}{x_2 - x_1}\). For a vertical line, \(x_2 - x_1 = 0\), and division by zero is undefined.

Line 2

• Falls from left to right:

When a line falls from left to right, the slope is negative. If we take two points \((x_1,y_1)\) and \((x_2,y_2)\) on the line with \(x_2>x_1\), then \(y_2 < y_1\). So, \(m=\frac{y_2 - y_1}{x_2 - x_1}<0\) (since numerator is negative and denominator is positive).

Line 3

• Horizontal line:

A horizontal line has a slope of zero. For a horizontal line, \(y_2 - y_1 = 0\). Using the slope formula \(m=\frac{y_2 - y_1}{x_2 - x_1}\), we get \(m = 0\) (since numerator is zero and denominator is non - zero).

Line 4

• Rises from left to right:

When a line rises from left to right, the slope is positive. If we take two points \((x_1,y_1)\) and \((x_2,y_2)\) on the line with \(x_2>x_1\), then \(y_2>y_1\). So, \(m=\frac{y_2 - y_1}{x_2 - x_1}>0\) (since both numerator and denominator are positive).

Answer:

Line 1: Undefined, Line 2: Negative, Line 3: Zero, Line 4: Positive