. 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.
