Exercise 7 Page 334

Consider the given equation of a line. y=3x+2 When lines are parallel, they have the same slope. Because of this, we know that all lines that are parallel to the line whose equation is given, will have a slope of 3. We can write a general equation in slope-intercept form for these lines. y=3x+ b We are asked to write the equation of a line parallel to the given equation that passes through the point ( 1, 3). By substituting this point into the above equation for x and y, we will be able to solve for the y-intercept b of the parallel line.

y=3x+b

SubstituteII

x= 1, y= 3

3=3( 1)+b

▼

Solve for b

Multiply

Multiply

3=3+b

SubEqn

LHS-3=RHS-3

0=b

RearrangeEqn

Rearrange equation

b=0

Now that we have the y-intercept, we can write the parallel line to y=3x+2 through (1,3). y=3x+ 0 ⇔ y = 3x