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Equations of Parallel Lines Practice

Practice Problem #1

Give the slope of each line. Are the lines parallel?

Two lines. The first line has points at (-1, -1) and (0, 1). The second line has points at (1, 0) and (0, -3)

Slope of line a ___

Answer: 2

Slope of line b ___

Answer: 3

Are they parallel?

Answer: no

Practice Problem #2

Give the slope of each line. Are the lines parallel?

Two lines. The first line has points at (0, 1) and (1, 0). The second line has points at (-2, 0) and (0, -2)

Slope of line a ___

Answer: -1

Slope of line b ___

Answer: -1

Are they parallel?

Answer: yes

Practice Problem #3

Are the lines parallel?

y = 3x + 4 and y = 3x - 2

Answer: yes; Since these equations are in slope intercept format, you can use the coefficient of the x-term as slope. Both of the coefficients here are three, so these lines are parallel.

Practice Problem #4

Are the lines parallel?

y - 3x = 5 and y = -3x + 2

Answer: no

Practice Problem #5

Find the equation of a line in slope intercept form that is parallel to the line y equals one-half x minus 3 and goes through the point (4, 1).

Start by finding the slope of the line.

Since the lines are parallelm what is the slope?

Answer: 0.5

Ok, now that we know that the slope of the line will be 1/2 we can plug the slope and point into the point slope equation.

y - y = m(x - x1)

y minus 1 = one half x - 2

Distribute the coefficient outside the parentheses to simplify.

y minus 1 equals one-half x minus 2

Answer: 1