Lesson: Forms of Linear Equations

Forms of Linear Equations

Slope-intercept
Point-slope
Standard

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​The slope formula:

​There are 4 types of slope.

Multiple Choice

A line with a positive slope looks like...

• A horizontal line

• A vertical line

• A line that goes uphill from left to right

• A squiggly line

Multiple Choice

A line with 0 slope looks like...

• A horizontal line

• A vertical line

• A slanted line

• A coordinate pair

Multiple Choice

What kind of slope does the graph have?

• Positive

• Negative

• 0

• Undefined

Multiple Choice

What type of slope?

• negative

• positive

• zero slope

• downward slope

Multiple Choice

What kind of slope does the graph have?

• Positive

• Negative

• 0

• Undefined

Multiple Choice

Which graph has a positive slope?

Multiple Choice

Which graph has an undefined slope?

Multiple Choice

What is the slope formula?

• $$\frac{y_2-y_1}{x_2-x_1}$$

• $$\frac{y_2-x_2}{x_1-y_1}$$

• $$\frac{x_2-x_1}{y_2-x_1}$$

• $$\frac{y_1-y_2}{x_1-x_2}$$

Multiple Choice

Find the Slope given:

(-1,-1) (2,7)

$$\left(x_1,y_1\right)\ \ \ \ \left(x_2,y_2\right)$$

• $$\frac{8}{3}$$

• $$\frac{3}{8}$$

• $$\frac{3}{4}$$

• 2

Multiple Choice

Find the Slope given:

(9,8) (6,5)

$$\left(x_1,y_1\right)\ \ \ \ \left(x_2,y_2\right)$$

• $$\frac{-3}{-3}$$

• 4

• 2

• $$\frac{2}{4}$$

Multiple Choice

What is the slope of the line that passes through these two points (0, -2) and (3, -4)?

• 2/3

• -2/3

• 3

• -2

Slope Y-intercept Form

• Y= mx + b

• of a line is: y=mx+b where m is the slope and b is the y-intercept. The y-intercept is always where the line intersects the y-axis, and will always appear as (0,b) in coordinate form.

• m is the slope

• b is the y-intercept

• m = 3/5, this is our slope

• b = 7, this our y - intercept

Multiple Choice

What does "m" represent in y=mx+b?

• y-intercept

• slope

• macaroni

• nothing

Multiple Choice

Which statement best describes "b"?

• x-intercept

• y- intercept

• Slope

• Bee

Multiple Choice

$$What\ is\ the\ y-intercept\ of\ the\ following\ equation\ y=-7x+5?$$  

• -7

• 5

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

Multiple Select

In slope-intercept form, what information is easy to find? Select all that apply.

• slope

• y-intercept

• rise over run

• a point on the line

Multiple Choice

$$What\ is\ the\ slope\ of\ the\ following\ equation\ y\ =\ -3x\ +\ 2$$  

• 1/3

• 3

• -3

• 2

Multiple Choice

Write the equation in  $$slope-intercept$$   given:

m = 3 and b = 5

• $$y=3x+5$$

• $$y=3x-5$$

• $$y=5x-3$$

• $$y=-3x+5$$

Multiple Choice

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

• 3

• 4x

• 4

• x

Multiple Choice

What is the y-intercept in the following equation:  y=-4x-5

• -4

• -4x

• 5

• -5

Point-Slope Form

• Point-slope is the general form y-y₁=m(x-x₁) for linear equations. It emphasizes the slope of the line and a point on the line (that is not the y-intercept).

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 Select

In point-slope form, what information is easy to find? Select all that apply.

• slope

• y-intercept

• rise over run

• a point on the line

Multiple Choice

Find the slope $$𝑦−6=-\frac{3}{7}(𝑥−9)$$  

• $$m=-6$$  

• $$m\ =\ -\frac{3}{7}$$  

• $$m=-15$$  

• $$m=-\frac{2}{3}$$  

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 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 given:

m = -6 and (-2, 5)

• $$y=-6x+5$$

• $$y+2=-6\left(x-5\right)$$

• $$y-5=-6\left(x-2\right)$$

• $$y-5=-6\left(x+2\right)$$

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

Write the equation of the line.
Slope = -4, passing through (-1, 5)

• y+5 = -4(x-1)

• y-5 = -4(x+1)

• y-5 = 4 (x-1)

• y = -4x - 9

Multiple Choice

For the equation
y + 1 = -3(x - 5),
the line contains the point (5, -1) and has a slope of?

• -1

• 1

• -3

• 5

Multiple Choice

What is the equation of the line that passes through (-2, 3) and has a slope of 4?

• y = -2x + 3

• y = 4x - 2

• y = 4x + 3

• y = 4x + 11

Standard Form

• Standard Form:  Ax + By = C This means  that we want the variables (x & y) to be on the left-hand side and the constant (6) to be on the right-hand side

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Multiple Choice

Which equation is written in standard form?

• 6y = x + 5

• y-1 = 7(x - 2)

• y = 1/2x + 15

• 2x + 3y = 18

Multiple Choice

The equation  $$3m+5n=14$$   is in what form?

• Point-Slope Form

• Slope-Intercept Form

• Standard Form

• m-n form

Multiple Choice

Which of these represents standard form of a linear equation?

• y - y₁ = m(x - x₁)

• Ax + By = C

• y = mx + b

Multiple Choice

Write in standard form.
4x - 2y + 3 = 7 - 4y

• 4x + 2y = 4

• 4x - 6y = 10

• 4x + 6y = 4

• 4x -2y = 4

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

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

Name the x- and y-intercepts for the equation:
5x - 3y = 15

• (3, 0) and (0, -5)

• (0, 3) and (-5, 0)

• (5, 15) and (15, 3)

• (0, -3) and (5, 0)

Match

Match the following

• y=mx+b

• Ax+By=C

• $$y-y_1=m\left(x-x_1\right)$$

• x=d

• y=b

slope-intercept form

standard form

point-slope form

vertical line

horizontal line

• slope-intercept form

• standard form

• point-slope form

• vertical line

• horizontal line