Question

Each of the line segments in the word MATH are numbered in the graph below. Find the slope (as a ratio of rise over run) of each line segment.

Answer 1

Line 1:
`\infty`

Line 2:
`-(4)/(3)`

Line 3:
`(4)/(3)`

Line 4:
`\infty`

Line 5:
`(7)/(4)`

Line 6 :
`-(7)/(3)`

Line 7: 0

Line 8: 0

Line 9:
`\infty`

Line 10:
`\infty`

Line 11: 0

Line 12:
`\infty`

Explanation:

Slope of line is given by the formula:

`\text{Slope = }\frac{\text{Change in } y\text{ coordinate}}{\text{Change in } x\text{ coordinate}}`

Line 1:

The change in
`x` coordinate is zero.

Therefore slope of line 1 is
`\infty`.

Line 2:

Change in
`y` coordinate = -4

Change in
`x` coordinate = 3

Slope =
`-(4)/(3)`

Line 3:

Change in
`y` coordinate = 4

Change in
`x` coordinate = 3

Slope =
`(4)/(3)`

Line 4:

The change in
`x` coordinate is zero.

Therefore slope of line 4 is
`\infty`.

Line 5:

Change in
`y` coordinate = 7

Change in
`x` coordinate = 3

Slope =
`(7)/(3)`

Line 6:

Change in
`y` coordinate = -7

Change in
`x` coordinate = 3

Slope =
`-(7)/(3)`

Line 7:

Change in
`y` coordinate = 0

Slope = 0

Line 8:

Change in
`y` coordinate = 0

Slope = 0

Line 9:

The change in
`x` coordinate is zero.

Therefore slope of line 9 is
`\infty`.

Line 10:

The change in
`x` coordinate is zero.

Therefore slope of line 10 is
`\infty`.

Line 11:

The change in
`y` coordinate is zero.

Therefore slope of line 11 is 0.

Line 12:

The change in
`x` coordinate is zero.

Therefore slope of line 12 is
`\infty`.