Parallel and Perpendicular Lines

Problem: 1

Is the following statement true or false? In a co–ordinate plane, every vertical line is perpendicular to every horizontal line.

Problem: 3

Is the following statement true or false? Two lines with negative slopes must be parallel.

Problem: 5

Check whether the graphs of the equations given below represent parallel lines. Explain your answer.

line a: y = –5x + 3

line b: y + 5x = –2

Problem: 7

Check whether the graphs of the equations given below represent parallel lines. Explain your answer.

line a: y = x + 7

line b: x – y = –2

Problem: 9

Test the two lines to see if they are perpendicular.

y = 5x – 3

Problem: 11

Test the two lines to see if they are perpendicular.

Problem: 13

Check if the graph of the pair of equations given below are parallel, perpendicular or neither.

y = 0.8x + 4

4y = –5x + 2

Problem: 15

Check if the graph of the pair of equations given below are parallel, perpendicular or neither.

y + 14 = 9

y + x = y + 5

Problem: 17

Write an equation of a line that is perpendicular to the given line:

y = –5x – 3

Problem: 19

Form the equation in the slope–intercept form of the line that passes through the given point and is parallel to the graph of the equation.

(3, 4), y = x + 7

Problem: 21

Form the equation in slope–intercept form of the line that passes through the given point and is parallel to the graph of the equation.

(6, 7), 9x – 8y = 24

Problem: 23

Form the equation of the line in–slope–intercept form that passes through the given point and is perpendicular to the graph of the given equation.

(7, –14), 3x –10y = 6

Problem: 25

Form the equation of the line in slope–intercept form that passes through the given point and is perpendicular to the graph of the given equation.

(7, –1), 4y +2x = 4

Problem: 27

Form the equation in slope–intercept form of the line that passes through the given point and is perpendicular to the graph of the given equation.

(0, –2), 6x – y = 4

Problem: 29

Are the three points listed below the vertices of a right triangle?

(5, 9), (7, 5), and (–1, 4)

Problem: 31

Refer to the graph. Determine the slopes of the sides to find if the figure is a parallelogram.

Problem: 33

Refer to the graph alongside. Compute the slopes of the sides to find if the figure is a parallelogram.

Problem: 35

Refer to the graph. Is the figure a rectangle? Use slopes.

Problem: 37

Refer to the graph. Is the figure a rectangle? Use slopes.

Problem: 39

Sketch the graph of the line y = 6x + 3. Find the equations of three other lines that, together with the line y = 6x + 3, would form a rectangle. Graph your rectangle.

Problem: 41

Find the value of k so that the graphs of 8y = kx – 4 and 6x + 24y = 12 are perpendicular.

Problem: 43

Find an equation for each line if the two lines are perpendicular.

Hotmath Practice Problems

Section 2-8

Parallel and Perpendicular Lines