Question 2
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Answer:
1) (-7, 8) and (-7, 0) - Undefined Slope.
2) (3, 5) and (-1, 2) - Positive Slope.
3) (2, 4) and (5, 1) - Negative Slope.
4) (6, -3) and (4, -3) - Zero Slope.
1) In the coordinates (-7, 8) and (-7, 0), we can see that the first number in both coordinates (the x point) is -7. If the x values are the same, that means that the line does not change at all horizontally/on the x-axis. The only solution to a line that passes through these points would be a vertical line. Vertical lines always have an undefined slope. To test, use the slope formula with the coordinates. y2 is the y in the second coordinate, y1 is the y from the first coordinate, x1 is the x from the first coordinate, and x2 is the x from the second coordinate.
0 - 8 = -8 and -7 - (-7) = -7 + 7 or 0. Any number divided by 0 is undefined.
2) In the coordinates (3, 5) and (-1, 2) there isn't any obvious abnormality in the coordinates that may cause undefined or 0. We can use the slope formula to find if it has a positive or negative slope.
2 - 5 = -3 and -1 - 3 = -4.
simplifies to 3/4, so the slope is positive.
3) (2, 4) and (5, 1) also don't have any repeating numbers in the coordinates so we can find the slope using the formula.
1 - 4 = -3 and 5 - 2 = 3
= -1, so the slope is negative.
4) (6, -3) and (4, -3) have the same y values in them, -3. If the y value stays constant then that means the line does not move along the y-axis. This means that it must be a straight line through 1 point on the y-axis. It is a horizontal line. The slope of a horizontal line is always 0 because is straight. You can check using the slope formula.
-3 - (-3) = -3 + 3 = 0 and 4 - 6 = -2.
= 0. The slope is 0.
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