Question

Consider and define which type of slope the line has.

Answer 1

Answer:

think of the numbers as the grid. zero being the middle and each square being 1 2 3 4 5 6 etc to the right of 0 are your positive, -1 -2 -3 etc move to the left of that line, your other access from zero goes up to positive one positive 2 positive 3 etc, from zero down you would be negative one negative 2 negative 3 etc

Answer 2

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.

$\frac{y2 - y1}{x2 - x1} = slope$        

$\frac{0 - 8}{-7 - (-7)} = slope$   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.

$\frac{y2 - y1}{x2 - x1} = slope$        

$\frac{2 - 5}{-1 - 3} = slope$   2 - 5 = -3 and -1 - 3 = -4.  $\frac{-3}{-4}$  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.

$\frac{y2 - y1}{x2 - x1} = slope$        

$\frac{1 - 4 }{5-2} = slope$   1 - 4 = -3 and 5 - 2 = 3   $\frac{-3}{3}$ = -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.

$\frac{y2 - y1}{x2 - x1} = slope$        

$\frac{-3 - (-3) }{4 - 6} = slope$   -3 - (-3) = -3 + 3 = 0 and 4 - 6 = -2. $\frac{0}{2}$ = 0. The slope is 0.

Let me know if you have any questions!