The equation which represents the perpendicular line is y = [tex]-\frac{4}{3}[/tex] x + [tex]\frac{13}{3}[/tex] ⇒ A
Step-by-step explanation:
Let us revise the relation between the slopes of the perpendicular lines
- The product of the slopes of the perpendicular lines is -1
- That means if the slope of one of them is m, then the slope of the other is
- reciprocal the slope of a line and change its sign to find the slope of the perpendicular line to it
The form of the linear equation is y = m x + b, where m is the slope of the line and b is the y-intercept (y at x = 0)
∵ The equation of the given line is y = [tex]\frac{3}{4}[/tex] x + 1
- Compare it with form of the equation above
∴ m = [tex]\frac{3}{4}[/tex] ⇒ slope of the given line
- To find the slope of the perpendicular line reciprocal it and
change its sign
∴ The slope of the perpendicular line = [tex]-\frac{4}{3}[/tex]
Let us write the equation of the perpendicular line
∵ y = m x + b
∴ y = [tex]-\frac{4}{3}[/tex] x + b
- To find b substitute x and y in the equation by the coordinates
of a point on the line
∵ The perpendicular line passes through the point (-5 , 11)
∴ x = -5 and y = 11
- Substitute it in the equation
∴ 11 = [tex]-\frac{4}{3}[/tex] (-5) + b
∴ 11 = [tex]\frac{20}{3}[/tex] + b
- Subtract [tex]\frac{20}{3}[/tex] from both sides
∴ [tex]\frac{13}{3}[/tex] = b
∴ y = [tex]-\frac{4}{3}[/tex] x + [tex]\frac{13}{3}[/tex]
The equation which represents the perpendicular line is
y = [tex]-\frac{4}{3}[/tex] x + [tex]\frac{13}{3}[/tex]
Learn more:
You can learn ore about the perpendicular lines in brainly.com/question/2601054
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