Answer:
y = 3x - 20
Step-by-step explanation:
First, we have to find the slope of the equation. We can do by taking the opposite reciprocal of the slope of the original line.
The opposite reciprocal of-1/3 is 3/1 or 3.
So, the slope of our equation will be 3. Our equation so far is:
y = 3x + b.
To find b, or the y-intercept of the line, we can simply substitute the given coordinates into the equation. If we replace x with 6 and y with -2 and solve the equation, we can find the value of b.
-2 = 3(6) + b
-2 = 18 + b
-2 - 18 = b
b = -20
So the equation is,
y = 3x -20.
To check our equation, we can again substitute the coordinates into the equation and solve. If both sides are equal, then the equation is correct.
-2 = 6(3) - 20
-2 = 18 - 20
-2 = -2
The two lines are perpendicular if a 90° angle is formed when they
intersect.
The equation of the line that passes through point Z(6, -2) and is perpendicular to the line [tex]y = -\dfrac{1}{3} \cdot x + 2[/tex] is ; y = 3·x - 20
Reason:
The equation of the required line is, y = 3·x - 20
The given point is Z(6, -2)
Perpendicular to the line, [tex]y = -\dfrac{1}{3} \cdot x + 2[/tex]
Solution:
The slope of a line perpendicular to another line having a slope, m, is [tex]-\dfrac{1}{m}[/tex]
The slope of the given line is [tex]-\dfrac{1}{3}[/tex]
The slope of the perpendicular line is therefore;
[tex]m = -\dfrac{1}{\left(-\dfrac{1}{3}\right)} = \dfrac{3}{1} = 3[/tex]
The point and slope form of the equation of the given line is therefore;
y - (-2) = 3·(x - 6)
y + 2 = 3·x - 3×6 = 3·x - 18
y = 3·x - 18 - 2 = 3·x - 20
y = 3·x - 20
The equation of the line that passes through point Z(6, -2) and is perpendicular to the line [tex]y = -\dfrac{1}{3} \cdot x + 2[/tex] is therefore;
y = 3·x - 20
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