Topic 2 Linear Equations Part 1

Topic 2 Linear Equations

Mrs. Palmer

Slope-Intercept Form

Slope Intercept Form

Shows you 2 pieces of information

1. Slope: also known as 'm' 
 $\frac{rise}{run}\ \ \ \ \ \ \frac{\Delta y}{\Delta x}\ \ \ \ \ \ \frac{y_2-y_1}{x_2-x_1}$  
2. y-intercept: also known as 'b'
(this is the constant in every  $y=mx+b$  

Multiple Choice

What is the slope of the following equation?

 $y=-\frac{1}{5}x+10$ 

• -1/5

• 1/5

• 5

• -5

Multiple Choice

What is the y-intercept of the following equation?

 $y=-\frac{1}{5}x+10$ 

•  $-\frac{1}{5}$  
  

• -10

•  $\frac{1}{10}$  
  

• 10

Multiple Choice

What is the slope of the following equation?

 $y=4x-3$ 

• -4

•  $\frac{1}{4}$   

•  $-\frac{1}{4}$  

• -3

• 4

Multiple Choice

What is the y-intercept of the following equation?

 $y=4x-3$ 

• -4

• 3

• -3

•  $-\frac{1}{3}$  

•  $\frac{1}{4}$  
  

Multiple Choice

Which graphs has a slope of 2 and a y-intercept of 3?

• Red

• Blue

• Green

• Purple

Point-Slope Form

Gives you 2 pieces of information...
1) An ordered pair

 $\left(x_1\ ,\ y_1\right)$  

2) Slope

Poll

True or False:
The ordered pair in this equation

 $y-3=2\left(x-4\right)$  is (4,3)

• True

• False

Point-Slope Form

 $y-y_1=m\left(x-x_1\right)$  

What is the ordered pair and the slope for the following equation? $y-5=-2\left(x-3\right)$  

 $y-y_1=m\left(x-x_1\right)$  

 $y-5=-2\left(x-3\right)$  

 $y-5\ =\ -2\left(x-3\right)$ 

 $m\ =\ -2\ or\ -\frac{2}{1}$  

 $\left(x_1\ ,\ y_1\right)=\left(3,5\right)$  

Multiple Select

What is the slope and ordered pair of the following point-slope equation?

 $y+2=3\left(x-4\right)$  

•  $m\ =3$  

•  $m=\frac{1}{3}$  

•  $\left(-4,2\right)$  

•  $\left(4,\ -2\right)$  

Multiple Select

What is the slope and ordered pair of the following Point-Slope Equation?

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

•  $m=\frac{1}{2}$  

•  $m=-\frac{1}{2}$  

•  $\left(4,3\right)$  

•  $\left(-4,\ -3\right)$  

Standard Form

 $Ax+By=C$  

helps you find the x-intercept and y-intercept quickly!

Standard Form:

•  $2x+4y=16$  

•  $A=2,B=4,C=16$ 

x-Intercept (when y=0) 

 

•  $2x+4y=16$  
  

•  $2x=16$  (divide both sides by 2)

•  $x=8$  

•  $\left(8,0\right)$  

y-Intercept (when x = 0)

 

•  $2x+4y=16$  
  

•  $4y=16$  (divide both sides by 4)

•  $x=4$  

•  $\left(0,\ 4\right)$  

Graph the two ordered pairs and connect with a straight line.  $(8,0)\ and\ (0,4)$  

 

Multiple Choice

Which Graph Represents this Standard Form Equation?

 $4x+3y=12$  

Multiple Choice

Which Graph Represents this Standard Form Equation?

 $2x+8y=8$  

Multiple Choice

Find the slope from the table.

• -4
• 1
• 4
• -2

Multiple Choice

What is the equation of the line in the graph?

• y = 3
• x = 3
• x = 0

Multiple Choice

Give the equation for the graph

• y = 5x - 3
• y = 4x + 2
• y =-2x + 5
• y = - 2x + 4

Multiple Choice

What letter represents the slope of a line in the equation y = mx + b?

• y
• m
• x
• b

Multiple Choice

What is the equation for the line that passes through the points (4,2) and (0,6)?

• y = x + 6
• y = -2x + 2
• y = -x - 6
• y = -x + 6

Multiple Choice

What is the slope of the line passing through the points (3,5) and (-1,7)?

• -1/2
• -1
• -2
• 1/2

Multiple Choice

What does the "b" stand for in y=mx+b?

• slope
• x-intercept
• y-intercept

Multiple Choice

Find the x and y intercepts
4x - 5y = 40

• x intercept is 10 
  y intercept is 8
• x intercept is 10
  y intercept is 20
• x intercept is 8
  y intercept is 10
• x intercept is 10
  y intercept is -8

Multiple Choice

Give the x-intercept
3x + 8y = 24

• (8, 0)
• (0, 8)
• (3, 0)
• (0, 3)

Multiple Choice

Name the x- and y-intercepts for the equation:
2x + y = 6

• (0, 3) and (6, 0)
• (0, -3) and (-6, 0)
• (3, 0) and (0, 6)
• (-3, 0) and (0, -6)

Multiple Choice

What is the formula for Point-Slope Form?

• y - y₁ = m(x - x₁)
• y = mx + b
• y + y₁ = m(x + x₁)
• y = mx - b

Multiple Choice

What is the formula to Slope-Intercept Form?

• y = mx + b
• y - y₁ = m(x - x₁)
• x = my + b
• funky chickens

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)

Multiple Choice

Which of these represents slope-intercept form of a linear equation?

• y - y₁ = m(x-x₁)
• Ax + By = C
• y = mx + b
• y=kx

Multiple Choice

Which of these represents point-slope form of a linear equation?

• y - y₁ = m(x - x₁)
• Ax + By = C
• y = mx + b
• y=kx

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

Are these two lines parallel, perpendicular or neither?
y = -1/3x - 5
y = 1/3x + 2

• Parallel
• Perpendicular
• Neither

Multiple Choice

The slopes of parallel lines are...

• the same

• opposite

• always different

Multiple Choice

Find the slope

• -5/3
• -3/5
• 5/3
• 3/5