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The graphs of the two lines 4X = 3y + 23 and 4y + 3x = -19
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GPT 3.5
To graph the two lines, we can rewrite the equations in slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept.
1) 4x = 3y + 23
Rearranging the equation:
3y = 4x - 23
Dividing both sides by 3:
y = (4/3)x - 23/3
2) 4y + 3x = -19
Rearranging the equation:
4y = -3x - 19
Dividing both sides by 4:
y = (-3/4)x - 19/4
Now that we have the equations in slope-intercept form, we can plot the lines.
Line 1: y = (4/3)x - 23/3
The slope of this line is 4/3, which means for every 3 units we move in the x-direction, we move 4 units in the y-direction. The y-intercept is -23/3.
Line 2: y = (-3/4)x - 19/4
The slope of this line is -3/4, meaning for every 4 units we move in the x-direction, we move 3 units in the negative y-direction. The y-intercept is -19/4.
Now, we can plot the lines on a graph:
Graph image: https://www.wolframalpha.com/input/?i=plot+4x+%3D+3y+%2B+23+and+4y+%2B+3x+%3D+-19
1) 4x = 3y + 23
Rearranging the equation:
3y = 4x - 23
Dividing both sides by 3:
y = (4/3)x - 23/3
2) 4y + 3x = -19
Rearranging the equation:
4y = -3x - 19
Dividing both sides by 4:
y = (-3/4)x - 19/4
Now that we have the equations in slope-intercept form, we can plot the lines.
Line 1: y = (4/3)x - 23/3
The slope of this line is 4/3, which means for every 3 units we move in the x-direction, we move 4 units in the y-direction. The y-intercept is -23/3.
Line 2: y = (-3/4)x - 19/4
The slope of this line is -3/4, meaning for every 4 units we move in the x-direction, we move 3 units in the negative y-direction. The y-intercept is -19/4.
Now, we can plot the lines on a graph:
Graph image: https://www.wolframalpha.com/input/?i=plot+4x+%3D+3y+%2B+23+and+4y+%2B+3x+%3D+-19