Question

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

Explanation:

Step1: Recall slope - rise over run concept

The slope \(m=\frac{\Delta y}{\Delta x}\), where \(\Delta y\) is the change in the \(y\) - coordinate and \(\Delta x\) is the change in the \(x\) - coordinate between two points on the line.

Step2: Analyze Line 1

As \(x\) increases, \(y\) decreases. So, \(\Delta x>0\) and \(\Delta y < 0\), then \(m=\frac{\Delta y}{\Delta x}<0\). The slope of Line 1 is negative.

Step3: Analyze Line 2

The \(y\) - value remains constant as \(x\) changes. So, \(\Delta y = 0\) and \(\Delta x
eq0\), then \(m=\frac{\Delta y}{\Delta x}=0\). The slope of Line 2 is zero.

Step4: Analyze Line 3

As \(x\) increases, \(y\) decreases. So, \(\Delta x>0\) and \(\Delta y < 0\), then \(m=\frac{\Delta y}{\Delta x}<0\). The slope of Line 3 is negative.

Step5: Analyze Line 4

The \(x\) - value remains constant as \(y\) changes. So, \(\Delta x = 0\) and \(\Delta y
eq0\), then \(m=\frac{\Delta y}{\Delta x}\) is undefined. The slope of Line 4 is undefined.

Answer:

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