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Pearson Geometry Common Core, 2011

PG

Pearson Geometry Common Core, 2011 View details

Cumulative Standards Review

Exercise 22 Page 214

What do parallel lines have in common?

y=0.5x+4.5

Practice makes perfect

Our goal is to find the equation of the line passing through the point (- 3,3) and is parallel to the line given in the diagram. Let's choose two points that we can use to write an equation of the line. Looking at the diagram, we can choose the y-intercept, (0,1.5), and the x-intercept, (-3,0).

Using these points, we can find the slope of the given line.

m=y_2-y_1/x_2-x_1

SubstitutePoints

Substitute ( 0,1.5) & ( -3,0)

m=0- 1.5/-3- 0

Subtract terms

m=-1.5/-3

Calculate quotient

m=0.5

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 0.5. We can write a general equation in slope-intercept form for these lines. y= 0.5x+ b We are asked to write the equation of a line parallel to the one with given equation that passes through the point ( - 3, 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=0.5x+b

x= -3, y= 3

3=0.5( -3)+b

▼

Solve for b

Multiply

3=-1.5+b

LHS+1.5=RHS+1.5

4.5=b

Rearrange equation

b=4.5

Now that we have the y-intercept, we can write the parallel line to the line from the diagram through (- 3,3). y= 0.5x+ 4.5