Math Unit 5

(BIG GRAPH) Which is the best description for the lines m and k? A) parallel B) perpendicular C) intersecting and parallel D) intersecting but not perpendicular

Find the slope of each line. Lines that are parallel will have the same slope and lines that are perpendicular will have opposite reciprocals. The slope of both lines m is -4. Since their slopes are the same the best description for the lines is parallel.

What is the slope for the line PERPENDICULAR to the line shown in the graph? A) -3 B) -1/3 C) 3 D) 1/3

The slope for the line perpendicular to the above is -1/3. The slope of the line above is 3. The slope of the line perpendicular to it is the opposite reciprocal of 3.

Find the equation of the line that is perpendicular to the line y = 4 and passes through the point (−2, 1). A) x = −2 B) y = −1 C) y = 1 D) x = 2

A) x = −2 The line perpendicular to y = 4 will be a vertical line through the point (−2, 1). The equation of the vertical line is x = −2.

Equation A: 3x + y = 6 Equation B: 6x - 2y = 4 Equation C: y = 3x - 2 Equation D: y = 13x + 7 Which two lines are perpendicular? A) A and B B) B and C C) A and D D) C and D

C) A and D Perpendicular lines have slopes that are opposite reciprocals. Equation A has a slope of -3, equation B has a slope of 3, equation C has a slope of 3, and equation D has a slope of - 13 3 and -13 are opposite reciprocals, so equations A and D are perpendiculars.

Write an equation of the line that is parallel to y = 1 2 x + 3 and passes through the point (10, -5). A) y = 2x - 15 B) y = -2x + 15 C) y = - 1/2x D) y = 1/2x - 10

Solution: y = 1/2x - 10. Parallel lines have the same slope. Therefore, the slope of the line is 1/2 . When we solve for the y-intercept, the result is -10.

Write the equation of the perpendicular bisector of AB. A) y = 5 3 x + 3 B) y = 3 5 x + 3 C) y = - 3 5 x + 3 D) y = - 5 3 x + 1

The solution is y = 3 5 x + 3. We must first determine the midpoint of segment AB using the midpoint formula. The result is (2.5, 4.5). We also know that the slope of segment AB is - 5 3 . Therefore, the slope of the perpendicular bisector must be 3 5 . You can then plot the line or use algebra to determine the y-intercept. 4.5 = 3 5 (2.5) + b b = 3 So, y = 3 5 x + 3 is the correct equation.

Which is true of the slopes of parallel lines? A) They are equal. B) They are opposites. C) They are additive inverses. D) The are opposite reciprocals.

A) They are equal.

Write an equation in slope-intercept form of the line perpendicular to y = 3x + 4 that passes through the point (3, 4). A) y = 3x - 5 B) y = 3x + 5 C) y = 1/3x + 5 D) y = -1/3x + 5

y = -1/3x + 5 slope-intercept form: y = mx + b The slope of perpendicular lines are negative reciprocals. Thus, m = -1/3. y = mx + b 4 = -1/3 (3) + b 4 = -1 + b b = 5 therefore, y = -1/3x + 5

Find the equation of a line parallel to y - 5x = 10 that passes through the point (3, 10). (answer in slope-intercept form) A) y = 5x - 5 B) y = 5x + 5 C) y = -5x - 5 D) y = 1/5x - 5

y = 5x - 5 y - 5x = 10 y = 5x + 10 Parallel lines have the same slope. Thus, the slope is 5. y = 5x + b 10 = 5(3) + b 10 = 15 + b b = -5 Thus, y = 5x - 5

Write an equation of the line that passes through the point (8, -1) and is perpendicular to the line pictured. A) y = 4x B) y = 4x + 1 C) y = -1/4x D) y = -1/4x + 1

y = -1/4x + 1 The slope (rise/run) of the graphed line is 4/1= 4. Therefore, the slope of the perpendicular line is the negative reciprocal, -1/4. Now, we can plug in x=-1, y=8, and m=-1/4 into y = mx + b and solve for b.-1 = (-1/4)(8) + b-1 = -2 + b b = 1 Thus, the equation of the perpendicular line is y = -1/4x + 1.

Write the equation of the perpendicular bisector of CD. A) y = -x + 6 B) y = x + 1/2 C) y = 1/2x + 6 D) y = -x + 1/2

The solution is y = -x + 6. We must first determine the midpoint of segment CD using the midpoint formula. The result is (2.5, 3.5). We also know that the slope of segment CD is 1. Therefore, the slope of the perpendicular bisector must be -1. You can then plot the line or use algebra to determine the y-intercept. 3.5 = -1(2.5) + b b = 6 So, y = -x + 6 is the correct equation.

Find the equation of the line parallel to the line graphed that passes through the point (1,1). A) y = 2x + 1/2 B) y = -2x + 1/2 C) y = 1/2x + 1 D) y = 1/2x + 1/2

The solution is y = 1/2x + 1/2 . By counting rise/run we see that the line has a slope of 1/2 . Since parallel lines have the same slope we use 1/2 for the slope and the point (1,1) to solve for b using y = mx + b. The resulting value for b is 1/2.

Consider the line in the coordinate plane that passes through the point (-7, -3) and the origin. Find the slope of a line perpendicular to the line described. A) -1/3 B) -3/7 C) -7/3 D) 3/7

-7/3 Use the formula: AB = y2 - y1 x2 - x1 M(-7, -3),(0,0) = 3/7 Perpendicular lines have slopes that are negative reciprocals of each other. thus, -7/3

Find the equation of a line parallel to y - 5 = 6x - 10 that passes through the point (4, 10). (answer in slope-intercept form) A) y = 6x - 14 B) y = 6x + 14 C) y = -6x - 14 D) y = 1/6x - 14

y = 6x - 14 Parallel lines have the same slope. Thus, the slope is 6. y = 6x + b 10 = 6(4) + b 10 = 24 + b b = -14 Thus, y = 6x - 14

Write an equation of the line that is perpendicular to y = 1/2x + 3 and passes through the point (10, -5). A) y = -2x + 15 B) y = 2x - 15 C) y = -2x - 5 D) y = - 1/2x

Solution: y = -2x + 15. Perpendicular lines have slopes that are opposite reciprocals of each other. Therefore, the slope of the line is -2. When we solve for the y-intercept, the result is 15.

Write an equation of the line that is perpendicular to 3x + 9y = 7 and passes through the point (6, 4). A) y = 3x - 14 B) y = 3x + 4 C) y = -3x + 16 D) y = 1/3x - 2

Solution: y = 3x - 26. First put the original equation in slope-intercept form: y = - 1/3x + 7/9 . Perpendicular lines have slopes that are opposite reciprocals of each other. Therefore, the slope of the line is 3. When we solve for the y-intercept, the result is -14.

Sara is trying to find an equation for a line that passes through (5, 2) and is perpendicular to 3x + 2y = 15. Explain the steps that Sara could take to determine the equation. A) Write 3x + 2y = 15 in slope-intercept form. Then, substitute the slope of that line and the point (5, 2) into the point-slope formula. B) Write 3x + 2y = 15 in slope-intercept form. Then, substitute the reciprocal of the slope of that line and the point (5, 2) into the point-slope formula. C) Write 3x + 2y = 15 in slope-intercept form. Then, substitute the opposite reciprocal of the slope of that line and the point (5, 2) into the point-slope formula. D) Write 3x + 2y = 15 in slope-intercept form. Then, substitute the opposite reciprocal of the slope of that line and the point (0, 0) into the point-slope formula.

Write 3x + 2y = 15 in slope-intercept form. Then, substitute the opposite reciprocal of the slope of that line and the point (5, 2) into the point-slope formula. Perpendicular lines have opposite reciprocated slopes.