Question

Which equation represents the line that is perpendicular to y= 3/4x + 1 and passes through (-5, 11)

Answer 1

The equation which represents the perpendicular line is y = $-\frac{4}{3}$  x  +  $\frac{13}{3}$  ⇒ 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 = $\frac{3}{4}$ x + 1

- Compare it with form of the equation above

∴ m =  $\frac{3}{4}$  ⇒ 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 = $-\frac{4}{3}$

Let us write the equation of the perpendicular line

∵ y = m x + b

∴ y =  $-\frac{4}{3}$ 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 =   $-\frac{4}{3}$ (-5) + b

∴ 11 = $\frac{20}{3}$ + b

- Subtract  $\frac{20}{3}$  from both sides

∴ $\frac{13}{3}$ = b

∴ y =  $-\frac{4}{3}$  x  +  $\frac{13}{3}$

The equation which represents the perpendicular line is

y = $-\frac{4}{3}$  x  +  $\frac{13}{3}$

Learn more:

You can learn ore about the perpendicular lines in brainly.com/question/2601054

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