Exercise 26 Page 243

To write the equation of a line perpendicular to the given equation, we first need to determine its slope. Then, we will write a general equation and use the given point to determine the y-intercept.

The Perpendicular Line's Slope

Two lines are perpendicular when their slopes are opposite reciprocals. This means that the product of a given slope and the slope of a line perpendicular to it will be -1. m_1* m_2=-1 For any equation written in slope-intercept form, y= mx+b, we can identify its slope as the value of m. Let's consider the given line. y= -1/4x+3 We can see that the slope is - 14. By substituting this value into our opposite reciprocal equation for m_1, we can solve for the slope of a perpendicular line, m_2.

m_1 * m_2 = - 1

Substitute

m_1= -1/4

-1/4* m_2 = - 1

▼

Solve for m_2

MoveRightFacToNumOne

1/b* a = a/b

-m_2/4=-1

MultEqn

LHS * (-4)=RHS* (-4)

m_2 = 4

Any line perpendicular to the given equation will have a slope of 4.

Writing the Perpendicular Line's Equation

With the slope m_2= 4, we can write a general equation in slope-intercept form for all lines perpendicular to the given equation. y= 4x+b By substituting the given point ( 2, 6) into this equation for x and y, we can solve for the y-intercept b of the perpendicular line.

y=4x+b

SubstituteII

x= 2, y= 6

6=4( 2)+b

▼

Solve for b

Multiply

Multiply

6=8 + b

SubEqn

LHS-8=RHS-8

-2=b

RearrangeEqn

Rearrange equation

b=-2

Now that we know that the y-intercept is -2, we can write the equation of the asked line. y= 4x-2 The obtained equation is the equation of a perpendicular line to y=- 14x+3 that passes through the point (2,6).