Exercise 4 Page 158

Practice makes perfect

When lines are parallel, they have the same slope. With this information, we know that all lines that are parallel to our given line will have a slope of 3. y= 3x-5 If we write the desired equation in slope-intercept form, y=mx+b, we can add this slope. y= 3x+ b To determine the value of b, we can use the fact that our line must pass through (1,5). Let's substitute x= 1 and y= 5 into the equation and solve for b.

y=3x+b

SubstituteII

x= 1, y= 5

5=3( 1)+b

▼

Solve for b

MultByOne

a * 1=a

5=3+b

SubEqn

LHS-3=RHS-3

2=b

RearrangeEqn

Rearrange equation

b= 2

Now that we have the y-intercept, we can conclude the line parallel to y=3x-5 that passes through (1,5). y= 3x+ 2

When lines are perpendicular, their slopes will be opposite reciprocals of one another. With this information, we know that all lines that are perpendicular to our given line will have a slope of - 13. Given Slope:& m_1=3 Opposite Reciprocal:& m_2=- 13 Now we can write a general equation for all lines with slope perpendicular to that of the given equation. y=- 1/3x+b Once again, to find b, we can substitute x= 1 and y= 5 into this equation.

y=- 1/3x+b

SubstituteII

x= 1, y= 5

5=- 1/3( 1)+b

▼

Solve for b

MultByOne

a * 1=a

5=- 1/3+b

AddEqn

LHS+1/3=RHS+1/3

5+1/3=b