for each line, determine whether the slope is positive, negative, zero, or undefined.\nline…

for each line, determine whether the slope is positive, negative, zero, or undefined.\nline 1\npositive\nnegative\nzero\nundefined\nline 2\npositive\nnegative\nzero\nundefined\nline 3\npositive\nnegative\nzero\nundefined\nline 4\npositive\nnegative\nzero\nundefined
Answer
Explanation:
Line 1
- Slope Concept: The slope (m=\frac{y_2 - y_1}{x_2 - x_1}). For a line going down - from - left - to - right, as (x) increases ((x_2>x_1)), (y) decreases ((y_2 < y_1)).
- Calculation: (m=\frac{\text{negative}}{\text{positive}}=\text{negative}).
Line 2
- Slope Formula: Let two points ((x_1,y)) and ((x_2,y)) on the line. Then (m = \frac{y - y}{x_2 - x_1}=0) (since the (y) - values are the same for any two points on a horizontal line).
Line 3
- Slope Formula: Let two points ((x,y_1)) and ((x,y_2)) on the line. Then (m=\frac{y_2 - y_1}{x - x}), and division by zero is undefined.
Line 4
- Slope Concept: For a line going up - from - left - to - right, as (x) increases ((x_2>x_1)), (y) also increases ((y_2>y_1)).
- Calculation: (m = \frac{\text{positive}}{\text{positive}}=\text{positive}).
Answer:
Line 1: Negative; Line 2: Zero; Line 3: Undefined; Line 4: Positive.