Question

Write an equation that represents each side of the figure. Write your equations in slope-intercept form. equation for the top side: y= equation for the top right side: y= equation for the bottom right side: y= equation for the bottom side: y= equation for the bottom left side: y= equation for the top left side: y=

Answer 1

Please, find the image of figure attached.

Answer:

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

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.