Write an equation that represents each side of the figure. Write ur equation in slope-intercept form.

1. Equation for the top side: y = 3

2. Equation for the top right side: y = - 3/2x + 6

3. Equation for the bottom right side: y = 3/2x - 6

4. Equation for the bottom side: y = - 3

5. Equation for the bottom left side: y = - 3/2x - 6

6. Equation for the top left side: y = 3/2x + 6

Step-by-step explanation: The slope-intercept form of the linear equations is y = mx + b, where m is the slope and b is the y-intercept.

1. Equation for the top side:

The top side is the horizontal (flat) portion of the figure (hexagon) that crosses the y-axis at y = 3.

Horizontal lines have slope m = 0.

The y-intercept is the point where the line crosses the y-axis. Hence, it is b = 3.

Substituting in the form y = mx + b, you get the equation y = 3.

Therefore, the equation that represents the top side is y = 3.

2. Equation for the top right side:

The top right side is the leaned line that goes from the point (4,0), on the x-axis, up to the point (2,3).

You can find the equation of a line using the coordinates of any two points.

First find the slope, m:

m = rise / run = Δy/Δx = (0 - 3) / (4 - 2) = -3/2

Now, use the point-slope equation:

y - y₁ = m (x - x₁)

You can use either point (4,0) or (2, 3).

Choose (4,0):

y - 0 = - 3/2 (x - 4)

Solve for y:

y = -3/2x + 6

Therefore, the equation that represents the top right side is y = -3/2x + 6.

3. Equation for the bottom right side:

The bottom right side is the leaned line that goes through the points (4,0) and (2, -3).

Again, you can find the equation using the coordinates of any two points.

First find the slope, m:

m = rise / run = Δy/Δx = [0 - (-3) ] / (4 - 2) = 3/2

Now, use the point-slope equation:

y - y₁ = m (x - x₁)

You can use either point (4,0) or (2, -3).

Choose (4,0):

y - 0 = 3/2 (x - 4)

Solve for y:

y = 3/2x - 6

Therefore, the equation that represents the bottom right side is y = 3/2x - 6.

4. Equation for the bottom side:

The bottom side is the horizontal line that intercept the y-axis at y = - 3.

The slope of a horizontal line is m = 0.

The y-intercept is the y value where the line crosses the y-axis: b = - 3.

Therefore, the equation for the bottom side is y = - 3

5. Equation for the bottom left side:

The bottom left side is the leaned line that goes through the points ( - 4,0) and ( - 2, -3).

Again, you can find the equation using the coordinates of any two points.

First find the slope, m:

This line is parallel to the top right side, hence they slopes are equal:

m = - 3/2

Now, use the point-slope equation:

y - y₁ = m (x - x₁)

You can use either point ( - 4,0) or ( - 2, -3).

Choose ( - 4,0):

y - 0 = - 3/2 [ x - ( - 4) ]

Solve for y:

y = - 3/2x - 6

Therefore, the equation that represents the bottom left side is y = - 3/2x - 6.

6. Equation for the top left side:

The top left side is the leaned line that goes through the points ( - 4,0) and ( - 2, 3).

Again, you can find the equation using the coordinates of any two points.

First find the slope, m:

This line is parallel to the bottom right side, hence they slopes are equal:

m = 3/2

Now, use the point-slope equation:

y - y₁ = m (x - x₁)

You can use either point ( - 4,0) or ( - 2, 3).

Choose ( - 4,0):

y - 0 = 3/2 [ x - ( - 4) ]

Solve for y:

y =  3/2x + 6

Therefore, the equation that represents the top left side is y = 3/2x + 6.

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7. d. 64

8. i. 32

9. c. 125

10. j. none of the above

11. d. 81

12. i. 216

13. e. none of the above

14. g. 240

15. e. none of the above

16. g. 32

17.   e. none of the above

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