A slope is also known as the gradient of a line. The point on the line perpendicular to the given line, passing through the given point that is also on the y-axis is (0, -3.6).
What is Slope?
A slope also known as the gradient of a line is a number that helps to know both the direction and the steepness of the line.
slope = (y₂-y₁)/(x₂-x₁)
The slope of the given line,
Slope, m₁ = (-4 - 6)/(-6 - 0) = -10/-6 = 5/3
Now, the slope of the line perpendicular to the given line is,
m₁ × m₂ = -1
5/3 × m₂ = -1
m₂ = -3/5
Further, the perpendicular line passes through the given point, therefore, the constant of the line can be found as,
y = (-3/5)x + c
-6 = (-3/5)4 + c
-6 = -12/5 + c
c = -6 + 12/5
c = (-30+12)/5
c = -18/5
Therefore, the equation of the line can be written as y=(-3/5)x-(18/5).
Now, since the line passes through the y-axis, therefore, the value of x is 0.
y = (-3/5)x - (18/5)
y = (-3/5)(0) - (18/5)
y = -18/5
y = -3.6
Hence, the point on the line perpendicular to the given line, passing through the given point that is also on the y-axis is (0, -3.6).
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