Linear Equations Part 2

Linear Equations

Part 2

Multiple Choice

 $y-y_1=m\left(x-x_1\right)$  is which of the following

• Point-Slope Form

• Slope-Intercept Form

• Standard Form

Multiple Choice

 $y=mx+b$   is which of the following

• Point-Slope Form

• Slope-Intercept Form

• Standard Form

Multiple Choice

 $Ax+By=C$   is which of the following

• Point-Slope Form

• Slope-Intercept Form

• Standard Form

How do you know which one to choose?

• Slope-Intercept Form

• Point-Slope Form

• Standard Form

Point-Slope Form

• 2 pieces of information: A Point and a Slope

•  $\left(x_1\ ,\ y_1\right)\ and\ 'm'$  

•  $\left(-1,\ -2\right),\ slope\ =\ -1$  

•  $y-\left(-2\right)=-1\left(x-\left(-1\right)\right)$  

•  $y+2=-1\left(x+1_{ }\right)$  

Slope-Intercept Form

•  $slope\ and\ y-intercept$  

•  $m,\ \left(0,\ y\right)$  

•  $y=-2x+4$  

•  $m=-\frac{2}{1}\ and\ y-int\ \left(0,\ 4\right)$  

Standard Form

• Helps find Intercepts Quickly

•  $Ax+By=C$  

•  $4x+12y=24$  

•  $x-intercept\ \left(x,\ 0\right)$  

•  $y-intercept\ \left(0,\ y\right)$  

Poll

 $y=2x-3$  Which method would you use to graph the problem?

• Point-Slope

• Slope-Intercept

• Standard Form

Poll

 $2x+10y=5$  Which method would you use to graph the problem?

• Point-Slope

• Slope-Intercept

• Standard Form

Poll

 $y-3=5\left(x-2\right)$  Which method would you use to graph the problem?

• Point-Slope

• Slope-Intercept

• Standard Form

Multiple Choice

 $3x+4y=12$  

Which graph best represent the following equation?

Multiple Choice

 $\left(10,\ 2\right)\ and\ \ \left(-9,\ 7\right)$  

What is the slope of the two given points?

•  $1$  

•  $5$  

•  $-\frac{5}{19}$  

•  $\frac{5}{19}$  

Multiple Choice

Write the equation of the line in Point-Slope form that goes through the point (10,5) and has a slope of -3

• $y-5=-3(x-10)$

• $y=-3x+35$

• $y+5=-3(x+10)$

• $y=-3x-35$

Parallel Lines

Same Slope-Different y-intercepts

Multiple Choice

Does the graph represent parallel lines?

• Yes

• No

Multiple Choice

 $y=-2x-2$  

Find the slope of a line parallel to function:

•  $y=-\frac{1}{2}x+2$  

•  $y=\frac{1}{2}x+2$  

•  $y=-2x+5$  

•  $y=-x+6$  

Multiple Choice

Which two equations below are parallel?

•  $y=2x+1\ and\ y=-\frac{1}{2}x+1$  

•  $y=2x+3\ and\ y=-2x+3$  

•  $y=2x-1\ and\ y=\frac{1}{2}x-1$  

•  $y=-x+4\ and\ y=-x+2$  

Multiple Choice

Which equation is parallel to: $y=\frac{5}{7}x+2$  

•  $y=-\frac{7}{5}x+1$  

•  $y=\frac{7}{5}x+4$  
  

•  $y=-\frac{5}{7}x-3$  
  

•  $y=\frac{5}{7}x+5$  
  

Multiple Choice

Which of the following equations has a graph PARALLEL to the line $y=4x+7$  

 and has an x-intercept of -2?

•  $y=4x-2$  
  

•  $y=4x+8$  
  

•  $y=\frac{7}{2}x+7$  
  

•  $y=-\frac{1}{4}x+\frac{1}{2}$  
  

Multiple Choice

Which of the following lines is PARALLEL to the graph of $5x+2y=8$ ?

•  $2x+5y=8$  
  

•  $5x-2y=6$  
  

•  $-10x-4y=7$  
  

•  $-10x+4y=9$  
  

Perpendicular Lines

form 90 degree angles and have opposite reciprocal slopes

Multiple Choice

What is the slope perpendicular to the equation: y=4x+3

• 
  

  $-\frac{1}{4}$
  

• $4$
  

• $4x$

• $\frac{1}{4}$
  

Multiple Choice

 $m=\frac{5}{8}$  

What slope is perpendicular to: 

•  $-\frac{5}{8}$  
  

•  $\frac{5}{8}$  
  

•  $-\frac{8}{5}$  
  

•  $\frac{8}{5}$  
  

Multiple Choice

 $y=\frac{3}{2}x+2$  

 $y=\frac{2}{3}x+6$  
These lines are...

• Parallel

• Perpendicular

• Neither

Multiple Choice

 $y=-\frac{2}{3}x+2$  

 $y=\frac{3}{2}x+9$  
These lines are...

• Parallel

• Perpendicular

• Neither

Multiple Choice

Are the lines parallel, perpendicular, or neither?
 $5x+4y=8$   $y=\frac{4}{5}x-3$  

• Parallel

• Perpendicular

• Neither

Multiple Choice

Are the lines parallel, perpendicular, or neither?
 $y=4x+7$   $y=-\frac{1}{4}x+2$  

• Parallel

• Perpendicular

• Neither

Multiple Choice

Slopes of perpendicular lines are...

• opposite reciprocals

• the same

• opposite

• always 7

It's a beautiful Day!

Have a great day ;)