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What is the slope of the line that goes through points (6,0) and (0, -8)?

Answer 1

Eva Abramson

# \qquad \qquad "slope of line between" \ ( 6, 0 ) \quad "and" \quad ( 0, -8 ) \ = \ 4/3 \ . #

# "Recall the definition of the slope of a line between two points: " #

# \quad "slope of line between" \ ( x_1, y_1 ) \quad "and" \quad ( x_2, y_2 ) \ = \ { y_2 - y_1} / { x_2 - x_1}. #

# "Applying this definition to our two given points, we get:" #

# \quad "slope of line between" \ ( 6, 0 ) \quad "and" \quad ( 0, -8 ) \ = \ { (-8) - (0) } / { (0) - (6) } #

# \qquad \qquad \qquad \qquad = \ { -8 } / { - 6 } \ = \ { (-2) (4) } / { (-2) (3) } \ = \ { color{red}cancel{ (-2) } (4) } / { color{red}cancel{ (-2) } (3) } \ = \ 4/3. #

# "So, we conclude:" #

# \qquad \qquad "slope of line between" \ ( 6, 0 ) \quad "and" \quad ( 0, -8 ) \ = \ 4/3 \ . #

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.