Into linear equations

Multiple Choice

Which of the following is a characteristic of a linear equation?

• Its graph is a straight line

• Variables have exponents greater than 1

• It always has two variables

• It cannot be graphed

Open Ended

Why do you think linear equations are important in mathematics and real life?

Fill in the Blanks

In the equation y = mx + b, the variable m stands for the

of the line.

Multiple Choice

In the slope-intercept form y = mx + b, what does the variable 'b' represent?

• The slope

• The x-intercept

• The y-intercept

• The origin

Multiple Choice

What type of slope does the graph have?

• Zero
• Undefined
• Negative
• Positive

Multiple Choice

Determine the slope and y-intercept.         y = 3/2x + 3

• slope: 5   y-intercept:  (0,3) 
• slope: 3/2   y-intercept:  (0,3) 
• slope:  4  y-intercept:  (0,3/2)
• slope: 1/5   y-intercept:  (0,5) 

Multiple Choice

Find the slope of the line.

• -5/4
• 5/4
• -4/5
• 4/5

Multiple Choice

Determine the slope and y-intercept.         y = 3/2x + 3

• slope: 5   y-intercept:  (0,3) 
• slope: 3/2   y-intercept:  (0,3) 
• slope:  4  y-intercept:  (0,3/2)
• slope: 1/5   y-intercept:  (0,5) 

Multiple Choice

How would you write the equation with a slope of 2/3 and a y-intercept of -3

• y=3/2x+3
• y=2/3-3
• y=2/3x-3
• y=2/3x+3

Multiple Choice

Find the slope of the line that passes through
(1, -19) and (-2, -7)

• -4
• 4
• 1/4
• -1/4

Multiple Choice

Find the slope of the line that passes through (-9, -6) and (-9, -10)

• 0
• Undefined
• -3
• -9

Multiple Choice

Find the slope of the line that passes through (10, -8) and (1, 12).

• 20/9
• -20/9
• 4/9
• 9/4

Multiple Choice

Which Graph is Linear?

• 1st
• 2nd
  2nd
• 3rd
• None

Multiple Choice

What is the x-intercept for the given graph?

• 1
• -2
• 2
• 1/2

Multiple Choice

Given the list of ordered pairs, what is the x-intercept?
(8,10),  (3, -4),  (0, 8), (4, -3), (9, 0)

• (8,10)
• 8, 3, 0, 4, 9
• (0,8)
• (9,0)

Multiple Choice

From the equation y = 3x + 18,  what is the value of the x-intercept?

• -6
• 6
• 18
• 3

Multiple Choice

What is the x-intercept shown on the graph?

• (2, 0)
• (-2, 0)
• (0, 3)
• (3, 0)

Multiple Choice

True or false:
The y-intercept of a function ALWAYS occurs where y is equal to zero.

• True
• False

Multiple Choice

True or false:
The x-intercept of a function ALWAYS occurs where y is equal to zero.

• True
• False

Multiple Choice

The slopes of parallel lines are...

• the same

• opposite

• always different

Multiple Choice

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

• Parallel
• Perpendicular
• Neither

Multiple Choice

Are these two lines parallel, perpendicular or neither?

y = -1/4 x - 5

y = 4x + 2

• Parallel

• Perpendicular

• Neither

Multiple Choice

Write a linear equation in slope intercept form of a line with a slope of -3 and y intercept of 0

• y=-3
• y=3x
• y=-3x
• x=-3

Multiple Choice

Write a linear equation in slope intercept form of a line with a slope of 12 and y intercept of 10

• y=12x-10

• y=10x+12

• y=12x+10

• x=10x-12

Multiple Choice

Which of the following is the correct format for the point-slope form of a linear equation?

• y = mx + b

• Ax + By = C

• y - y₁ = m(x - x₁)

• y = m(x - x₁) + b

Multiple Choice

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

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

Multiple Select

Select all of the following equations in point-slope form.

• y - 2 = 5(x - 2)

• 3x + 2y = 12

• y + 2 = 1/4(x + 4)

• y = 4x + 6

• 2y = 5x - 7

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

What is the equation in Point-Slope form

of the line that goes through

the point (6,1) and has a slope of -3?

• y - 6 = -3(x - 1)

• y + 6 = -3(x + 1)

• y - 1 = -3(x - 6)

• y + 1 = -3(x + 3)

Multiple Choice

The line with the equation

y + 1 = -3(x - 5),

contains the point (5, -1)

and has a slope of _______.

• -1

• 1

• -3

• 5

Multiple Choice

For the equation
y - 3 = 2(x + 4),
the line has a slope of 2 and contains what point?

• (-4, 3)
• (3, -4)
• (-3, -4)
• (-4, -3)

Multiple Choice

What is the point slope form equation of the graph given(use blue point in equation)

• y + 2 = $$\frac{3}{2}$$ (x + 2)
  

• y - 2 = $$\frac{3}{2}$$ (x - 2)

• y + 2 = - $$\frac{3}{2}$$ (x + 2)

• y - 2= - $$\frac{3}{2}$$ (x - 2)

Multiple Select

Which of the following statements are true about the standard form of a linear equation?

• A, B, and C are integers.

• A should be positive.

• It is written as y = mx + b.

• An example is 2x + 3y = 6.

Multiple Choice

What is the slope-intercept form of a line?

• Ax + By = C

• y = mx + b

• y - y1 = m(x - x1)

• y = Ax + By

Multiple Choice

Which of the following are written in standard form?

• y=3x-5
• 3x+16=5y
• 2/3 x + 9/13 y = 21
• 5x+7y=-12

Open Ended

Explain the process of converting a linear equation from point-slope form to slope-intercept form using an example.

Open Ended

Describe the steps required to convert a linear equation from standard form to slope-intercept form. Provide an example in your explanation.

Multiple Choice

Convert this equation into slope-intercept form. 3x + y = 12

• y = -3x +12
• x = y + 4
• x = y + 12
• y = 3x -12

Multiple Choice

Convert Point-Slope y - 5 = - 2( x + 3) to slope-intercept form

• y = -2x - 11

• y = -2x - 1

• y = -2x + 8

• y = -2x - 2

Multiple Choice

Convert Point-Slope y - 3 = 2( x - 5) to slope-intercept form

• y = 2x - 8
  

• y = 2x - 13

• y = 2x - 2

• y = 2x - 7

Multiple Choice

Convert Point-Slope y + 3 = 3( x - 5) to slope-intercept form

• y = 3x - 8
  

• y = 3x - 12

• y = 3x - 18

• y = 3x - 2

Multiple Choice

What equation represents point-slope form?

• y = mx + b

• y - y₁ = m ( x - x₁ )

• y = mx - b

• y + y₁ = m ( x + x₁ )

Multiple Choice

Which of the following is slope intercept form?

• Ax+By = C

• y-y₁=m(x-x₁)

• y=mx+b

• I don't know

Multiple Choice

Convert Point-Slope y + 5 = 3( x + 3) to slope-intercept form

• y = 3x + 4

• y = 3x + 14

• y = 3x - 2

• y = 3x + 8

Multiple Choice

Convert Point-Slope y - 1 = - 2( x - 4) to slope-intercept form

• y = -2x - 5

• y = -2x + 7

• y = -2x - 3

• y = -2x + 9

Multiple Choice

Is the following equation in slope-intercept form or point-slope form?
$$y=-\frac{1}{3}x-17$$  

• Point-Slope Form

• Slope-Intercept Form

Multiple Choice

Convert Point-Slope y - 4 = 3( x + 1) to slope-intercept form

• y = 3x + 7

• y = 3x -- 1

• y = 3x + 5

• y = 3x - 3

Multiple Choice

Convert Point-Slope y + 3 = -2( x + 2) to slope-intercept form

• y = -2x + 5
  

• y = -2x -- 1

• y = -2x + 1

• y = -2x - 7

Multiple Choice

Convert this equation into slope-intercept form. x + y = 4

• y = x + 4
• y = -x + 4
• x = -y + 4
• x= y - 4

Multiple Choice

Convert this equation into slope-intercept form. 2x + y = 41

• x = 2y + 41
• y = 2x -41
• y = -2x + 41
• x = y -39

Multiple Choice

Convert this equation into slope-intercept form.

• y=-3x+1

• y=3x+1

• y=1/3x+1

• y=-1/3x-1

Multiple Choice

Convert this equation into slope-intercept form.

• y=-4x-12

• y=4x+12

• y=-4x+12

• y=-4x+3

Multiple Choice

Solve for y:
2x + 2y = 6

• y = - x + 3
• y = x + 3
• y = 2x +6
• y = - 2x + 6

Multiple Choice

Solve for y: 
8x + 4y= 16

• y = -8x + 16
• y = 2x -4
• y = -2x + 4
• y = -8x + 12

Multiple Choice

Solve this equation for y:
$$-6x+3y=9$$  

• y = 2x + 9

• y = 6x - 3

• y = 2x + 3

• y = 6x + 9

Multiple Choice

Solve this equation for y:
$$10x\ -5y=30$$  

• y = 2x - 6

• y = -2x + 6

• y = -10x + 30

• y = 10x - 30

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Multiple Choice

Which of the following equations represents the same line as y = 2x + 1?

• y - 3 = 2(x - 1)

• y = 3x + 1

• 2x - y = -1

• y = 2x - 1

Multiple Choice

Which of the following are examples of linear equations in standard form?

• 2x - y = -1

• y = 2x + 1

• C = (5/9)(F - 32)

• y = -10x + 100

Open Ended

Explain how linear equations can be used to model real-life situations, using examples from the slide.

Open Ended

Describe the process of converting a linear equation from slope-intercept form to standard form. Why might you want to do this?

Fill in the Blanks

The equation y = mx + b is known as the

form of a linear equation.

Open Ended

How would you explain the importance of linear equations in real-life situations?

Multiple Choice

What is a key characteristic of a linear equation?

• Its graph is a straight line

• It has variables with exponents greater than 1

• It always passes through the origin

• It only has one variable