Chapter 5 Review

Chapter 5 Test Review

Writing Linear Equations

Slope Intercept formula

•  $y\ =\ mx\ +\ b$  

•  $m=slope\ =\ \frac{y_2-y_1}{x_2-x_1}$  

•  $b\ =\ y\ intercept$  

Given a graph

• Slope intercept formula
  

•  $y\ =\ mx+b$  
  

Find slope and y-intercept

•  $m\ =\ slope\ =\ \frac{rise}{run}=\frac{5}{5}=1$  
  

•  $b\ =\ -5$  
  

m = 1 and b = - 5 so

•  $y\ =1x\ -\ 5$  

•  $y\ =1x\ +-\ 5$  

Multiple Choice

Write the equation of the line.

• y = -2/3x + 4

• y = 2/3x + 4

• y = 3/2x + 4

• y = -3/2x + 4

Multiple Choice

What is the equation of this line?

• y = 2x +2

• y = 2x -2

• y = -x + 2

• Cannot be Determined

Multiple Choice

Write the equation of the line.

• y = -1/3x - 2

• y = 1/3x - 2

• y = 3x - 2

• y = -3x - 2

Multiple Choice

Write the equation for the line in slope-intercept form.

• y= -1x+3

• y= 4x+3

• y=1/4x+3

• y= -4x+3

Special cases: Graphs

• Slope intercept formula
  

•  $y\ =\ b$  
  

• through the y-axis
  

• y is always 5
  

Special cases: Graphs

• Slope intercept formula
  

•  $x=\ a$  
  

• through the x-axis
  

• x is always - 5
  

Multiple Choice

What is the equation of this line?

• 0

• undefined

• y = -2

• x = -2

Multiple Choice

What is the equation of the line in the graph?

• y = 3

• x = 3

• x = 0

Multiple Choice

Which equation matches the graph?

• y = 5

• y = -5

• x = -5

• x = 5

Multiple Choice

Which equation matches the graph?

• y = 5

• y = -5

• x = -5

• x = 5

Multiple Choice

Which graph represents x=2?

• A

• B

• C

• D

Given  $slope\ =\ -3\ \ \ and\ \ \ y-intercept\ =\ 5$  

•  Equation of the line is
  

•  $y=-3x+5$  
  

Given  $m\ =\ -\frac{2}{3}\ \ and\ \ b\ =\ -1$  

• Equation of
  

•  $y\ =-\frac{2}{3}x\ -\ 1$  
  

Multiple Choice

What is the equation of a line with a slope of 2 and a y-intercept of -5?

• y = 5x - 2

• y = 2x - 5

• y = -2x - 5

• y = 2x + 5

Multiple Choice

What is the equation of a line with a slope of 4 and a y-intercept of 2?

• y = -4x + 2

• y = -2x + 4

• y = 4x + 2

• y = 2x + 4

Multiple Choice

What is the equation of a line when m = -3 and b = 5?

• y = -3x + 5

• y = -3x - 5

• y = 5x + 3

• y = -5x - 3

Multiple Choice

If m=3 and b=6, what is the correct slope intercept equation?

• y=3-6

• y=3x-6

• y=3x+6

• y=6x+3

Point Slope formula

•  $y-y_1\ =\ m\left(x\ -x_1\right)$  

•  $m=slope\$  

•  $\left(x_1,\ \ y_1\right)\ is\ any\ point\ on\ the\ line$  

 $y-y_1\ =\ m\left(x\ -x_1\right)$  

•  $y\ -\left(-4\right)\ =\ -\frac{3}{2}\left(x-2\right)$  
  

•  $y\ +4\ =\ -\frac{3}{2}\left(x-2\right)$  
  

 $y-y_1\ =\ m\left(x\ -x_1\right)$  

•  $y\ -5=\ 0\left(x+3\right)$  
  

•  $y\ -5\ =0x\ +\ 0\$  
  

•  $y\ -\ 5=0$ 
  

Special Case

• if m = undefined, then graph is a vertical line
  

• Vertical lines go through x axis
  

• So this equation is x = 5
  

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

Multiple Choice

Write the equation in point-slope form of the line that passes through the given point and has the given slope.
(4, -7); m = -1/4

• y + 7 = -1/4(x - 4)
• y - 4 = -1/4(x + 7)
• y + 7 = 4(x - 4)
• y - 7 = -1/4(x - 4)

Multiple Choice

Write an equation in point slope form of equation of line

point (7,10) and has a slope of -2?

• y-10 = -2(x+7)

• y-10 = -2(x-7)

• y+10 = -2(x+10)

• y -10 = -2x+2

Multiple Choice

Write equation of a line in point slope form that passes through (3,8) and has a slope of 5?

• y-8=5(x-3)

• y=5x+8

• y-3=5(x-8)

• y-y₁₌ m(x-x₁₎

Point Slope formula

•  $y-y_1\ =\ m\left(x\ -x_1\right)$  

•  $m=slope$  

•  $Use\ any\ point\ on\ the\ line\ as\ \left(x_1,\ \ y_1\right)\$  

Point Slope formula

•  $y-3\ =\ -2\left(x\ -1\right)$  

•  $m=-2$  

•  $Ordered\ pair\ is\ \left(1,\ \ 3\right)\$  

Point Slope formula

•  $y+7\ =\ -\left(x\ +8\right)$  

•  $m=-1$  

•  $Ordered\ pair\ is\ \left(-8,\ \ -7\right)\$  

Point Slope formula

•  $y-4\ =\ -\frac{1}{2}\left(x\ +8\right)$  

•  $m=-\frac{1}{2}$  

•  $Ordered\ pair\ is\ \left(-8,\ \ 4\right)\$  

Multiple Choice

Identify the slope and ordered pair from the equation: y – 4 = – (x + 2)

• m = 1 ( - 2, 4 )

• m = - 1 ( - 2, 4 )

• m = - 1 ( 4, - 2 )

• m = - 1 ( 2, - 4 )

Multiple Choice

Identify the slope and ordered pair from the equation: y – 3 = –2 (x + 4)

• m = - 2 ( 3, - 4 )

• m = - 2 ( - 4, 3 )

• m = 2 ( - 4, 3 )

• m = 2 ( 3, - 4 )

Multiple Choice

Given y + 6 = 10( x - 9) , what is the point used to write this equation?

• (10, 9)

• (6, -9)

• (-6, 9)

• (9, -6)

Multiple Choice

What is the slope of the equation y - 2 = -6( x + 6)

• 2

• 6

• -2

• -6

Multiple Choice

For the equation

y - 4 = -1/3(x - 7),

what are the coordinates for the point?

• (4, 7)

• (-7, - 4)

• (7, 4)

• (-4, -7)

Point Slope formula given 2 points

•  $y-y_1\ =\ m\left(x\ -x_1\right)$  

•  $Find\ \ m=slope\ =\frac{y_2-y_1}{x_2-x_1}$  

•  $Use\ any\ point\ on\ the\ line\ as\ \left(x_1,\ \ y_1\right)\$  

Write  $y\ -y_1\ =\ m\left(x-x_1\right)$  

• Find slope or m:   $\frac{2-\left(-10\right)}{5-\left(-1\right)}=\frac{2+10}{5+1}=\frac{12}{6}=2$  
  

•  $\left(x_1,\ \ y_1\right)\ =\ \left(5,\ 2\right)$  
  

Write  $y\ -y_1\ =\ m\left(x-x_1\right)$  

•  $m\ =\ 2\ \ \ \ \ \ \ \left(x_1,\ \ y_2\right)\ =\ \left(5,\ 2\right)$  
  

•  $y\ -2\ =\ 2\left(x-5\right)$  

Write  $y\ -y_1\ =\ m\left(x-x_1\right)$  

• Find slope or m:   $\frac{5-3}{0-4}=\frac{2}{-4}=-\frac{1}{2}$  
  

•  $\left(x_1,\ \ y_1\right)\ =\ \left(4,\ 3\right)$  
  

Write  $y\ -y_1\ =\ m\left(x-x_1\right)$  

•  $m\ =-\frac{1}{2}\ \ \ \ \ \ \left(x_1,\ \ y_2\right)\ =\ \left(4,\ 3\right)$  
  

•  $y\ -3\ =\ -\frac{1}{2}\left(x-4\right)$  

Multiple Choice

Find the slope when given the following (3, 5) (-2, 0)

• 1

• -1

• -5/2

• 3

Multiple Choice

Write an equation in point-slope form of the line through the given points: ( 4, 0 ) , ( - 2, 1 )

• y - 0 = -5/6 ( x - 4)

• y - 0 = -2/3 ( x - 4)

• y - 0 = -1/6 ( x + 4)

• y - 0 = -1/6 ( x - 4)

Multiple Choice

Write an equation in point-slope form of the line that passes through the given points: ( - 3, - 2), (5, 3)

• y - 2 = 5/8 (x - 3)

• y + 2 = 5/8 (x + 3)

• y + 3 = 5/8 (x + 2)

• y - 3 = 5/8 (x - 2)

Multiple Choice

Write the equation in point-slope form for the line that contains the points

(3, -5) and (5, - 1)

• y - 5 = 2(x + 3)

• y + 5 = 2(x - 3)

• y - 3 = 2(x + 5)

• y + 3 = 2(x - 5)

Multiple Choice

Write the equation in point-slope form for the line that contains the points

(-2, -3), (4, 3)

• y - 3 = 1(x - 2)

• y + 3 = 1(x + 2)

• y -3 = -1(x + 2)

• y + 3 = -1(x - 2)

Slope intercept form: Given 2 points

• Find slope

• Find b or simplify point slope form

Find slope

•  $m=\frac{7-\left(-1\right)}{4-3}=\frac{7+1}{4-3}=\frac{8}{1}=8$  

• 
  

Find b with slope intercept
 $y=mx+b$  

•  $m=8$  (x, y) = (3, - 1)
  

• Solve for b
  

• -1 = 8(3) + b
  

• -1 = 24 + b
  

• -25 = b
  

Find b with point slope
 $y-y_1=m\left(x-x_1\right)$  

•  $m=8$  $\left(x_1,\ y_1\right)=\left(3,\ -1\right)$  
  

•  $y+1=8\left(x-3\right)$  
  

•  $y+1=8x-24$  

•  $y=8x-24-1$  

Multiple Choice

 Write the equation of the line that passes through the points (0, -5) and (4, 3)

• y=2x-5
• y=1/2x-5
• y=2x+5
• y=1/2x+5

Multiple Choice

What is the equation of the line that passes through (1, 4) and (2, 1)

• y = -3x + 1

• y = -3x + 4

• y = -3x - 7

• y = -3x + 7

Multiple Choice

What is the equation of the line that passes through (-1, -4) and (-2, -1)

• y = 2x - 1

• y = -2x - 4

• y = 3x - 7

• y = -3x - 7

Multiple Choice

Write the equation in slope intercept form of a line that passes through the given pair of points: (-2, -3), (4, 3)

• y =x + 1

• y = x - 1

• y = -x + 1

• y = -x - 1