Alg 1: Equations of Parallel and Perpendicular lines

Alg 1: Equations of Parallel and Perpendicular lines

Multiple Choice

 $y=2x+1$  

 $6x-3y=17$  

The lines are 

• parallel

• not parallel

They were parallel.

They had the same slope.

 $y=2x+1$  slope is 2

 $6x-3y=17$  slope is  $-\frac{a}{b}=-\frac{6}{-3}=2$  

y-intercepts are different -  $1\ and\ -\frac{17}{3}$  

Multiple Choice

Write the equation, in slope-intercept form, of the line that goes through  $\left(-3,2\right)$  and is parallel to the line  $y=\frac{4}{7}x+\frac{5}{7}$  

•  $y=\frac{5}{7}x$  

•  $y=\frac{4}{7}x+\frac{26}{7}$  

•  $y=-\frac{2}{3}x+\frac{5}{7}$  

•  $y=\frac{4}{7}x-\frac{12}{7}$  

Multiple Choice

The lines  $y=\frac{2}{3}x-8$  and  $y=\frac{3}{2}x-12$  are 

• parallel

• perpendicular

• neither

They were neither.

They had reciprocal slopes $\left(\frac{3}{2}\ and\ \frac{2}{3}\right)$  but they were not OPPOSITE reciprocals. Must be both to be perpendicular. 

Multiple Choice

The two lines  $5x-7y=11$  and  $7x+5y=23$  

• parallel

• perpendicular

• neither

They are perpendicular.

They are in standard form  $\left(ax+by=c\right)$  so the slope of each is  $-\frac{a}{b}$  .

One has a slope of  $\frac{5}{7}$  and the other is  $-\frac{7}{5}$  . They are opposite reciprocals. So they are perpendicular. 

Multiple Choice

If two lines are parallel their slopes are  ____________

• the same.
• negative reciprocals of each other.

Multiple Choice

If two lines are perpendicular to each other their slopes are ____________

• the same.

• negative reciprocals of each other.

Multiple Choice

Are these lines perpendicular?
y = 4x + 2
y = (-1/4)x + 12

• YES
• NO

Multiple Choice

Are these lines parallel?

y = (-1/2)x + 1

y = (1/2)x - 5

• YES

• NO

Multiple Choice

Are these lines parallel?
y = 12x + 4
y = 12x +14

• YES
• NO

Multiple Choice

Write an equation of a line that passes through the point (5,-1) and is parallel to the line y = (-3/5)x -3

• y = (-3/5)x + 2
• y = (-3/5)x -2
• y = (3/5)x + 2
• y = (5/3) + 2

Multiple Choice

Write an equation of a line that passes through the point (-2,3) and is parallel to the line x = 4

• y = -2
• y = 2
• x = 2
• x = -2

Multiple Choice

Write an equation of a line that passes through the point (7,10) and is perpendicular to the line y = (1/2)x - 9

• y = -2x - 24
• y = -2x + 12
• y = -2x  + 24
• y = (1/2)x - 12

Multiple Choice

Write an equation of a line that passes through the point (-2,3) and is perpendicular to the line x = 4

• y = 3
• x = -3
• y = -3
• x = 3