To determine the relationship between the two lines, we can first rearrange the given equations into slope-intercept form (y = mx + b):
Equation 1: 4x = 3y + 23
Rearranging, we have: 3y = 4x - 23
Dividing by 3: y = (4/3)x - 23/3
Equation 2: 4y + 3x = -19
Subtracting 3x from both sides: 4y = -3x - 19
Dividing by 4: y = (-3/4)x - 19/4
Comparing the slopes of the two lines, we see that (4/3) and (-3/4) are not equal, and therefore the lines are not identical.
To determine if the lines are perpendicular, we can compare the product of their slopes. The product of the slopes of two perpendicular lines is -1.
The slope of the first line is 4/3.
The slope of the second line is -3/4.
(4/3) * (-3/4) = -1
Since the product of the slopes is -1, we can conclude that the lines are perpendicular.
Therefore, the correct answer is:
D. The graphs of the two lines are perpendicular.
5. The graphs of the two lines 4x = 3y + 23 and 4y + 3x = -19
A. do not intersect.
C. intersect at (-2, 5)
B. are identical.
D. are perpendicular.
1 answer