Answer:
Perpendicular slope: -3/2
Y-value of the y-intercept: 6
Linear equation of the perpendicular line: y = -3/2x + 6
Step-by-step explanation:
Perpendicular lines have negative reciprocal slopes, which means that multiplying the slopes of both lines will result in -1.
Given the linear equation, y = 2/3x - 5/3, and the point, (0, 6):
Let m1 = slope of line 1
m2 = slope of the other line
Since the slope of y = 2/3x - 5/3 is 2/3, then the other line must have a slope of -3/2 because:
m1 × m2 = -1
[tex](\frac{2}{3}) (-\frac{3}{2}) = -1[/tex]
Therefore, the slope of the other line (m2) = -3/2.
The y-intercept is the y-coordinate of the point where the graph of the linear equation crosses the y-axis. The y-intercept is also the value of y when x = 0. The given point has coordinates (0, 6), which means that it is the y-intercept. Its y-coordinate, (b) = 6.
Therefore, given the slope m = -3/2, and the y-value of the y-intercept, b = 6, then the equation of the perpendicular line is: y = -3/2x + 6.
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