Standard Form - Part 1

Standard Form

By Mattison Johnson

Match

Find the x-intercept for each question!

Hint: Replace x with 0. Then solve for y.

• 2x + 3y = 5

• -3x + 2y = 1

• -4x - 2y = 6

x-intercept: 5/2

x-intercept: -1/3

x-intercept: -3/2

• x-intercept: 5/2

• x-intercept: -1/3

• x-intercept: -3/2

Multiple Choice

Ice cream comes in 1 qt. and 5 qt. containers. You need to purchase 17qts of ice cream for an ice cream social.

Which equation represents this scenario?

Note: x will represent the # of 1 qt containers. y will represent the # of 5 qt containers.

• 5x + 1y = 17

• 1x + 5y = 17

• y = 17x + 1

• y = x + 17

Multiple Select

Select all of the NON-integers.

• -1

• 0.3

• 4/2

• 1/2

• 0

Multiple Select

Select ALL of the appropriate Standard Form equations.

Ax + By = C

• y = 3x + 4

• 9x - 5y = 1

• 0.5x + 8y = 13

• 6x + 7y = 12

• y - 3 = 6(x-9)

Reorder

Order the steps for converting Standard Form to Slope-Intercept Form.

• Get the y-term by itself, via addition or subtraction.

• Get the y variable by itself, via division or multiplication.

• Check the final equation is in

  y = mx + b form.

1

2

3

• 1
• 2
• 3

Reorder

Now let's do the opposite!

Order the steps for converting Slope-Intercept Form to Standard Form.

Write $$y=\frac{2}{3}x\ +\ 2$$ in standard form, with integer coefficients.

• Move the x-term to y's side, via addition or subtraction.

  (Subtract -2/3x from both sides.)

  $$-\ \frac{2}{3}x\ +y=\ 2$$

• Eliminate the fraction by multiplying all terms by the denominator (3).

  -2x +3y = 6

• Check the final equation is in

  Ax + By = C form, with A, B, and C as integers.

1

2

3

• 1
• 2
• 3

Reorder

Now let's do the opposite!

Order the steps for converting Point-Slope Form to Standard Form.

$$𝑦+2=3(𝑥−4)$$

• Distribute the factor outside the parentheses (3).

  y + 2 = 3x - 12

• Move constants onto the same side, via addition or subtraction.

  (Subtract 2 from both sides)

  y = 3x - 14

• Move the x-term to y's side, via addition or subtraction.

  (Subtract 3x from both sides)

  - 3x + y = -14

• Check the final equation is in

  Ax + By = C form, with A, B, and C as integers.

1

2

3

4

• 1
• 2
• 3
• 4

Multiple Choice

To determine the SLOPE and y-INTERCEPT of an equation in standard form, like 2𝑥 + 3𝑦 = 5,

which type should you convert it to?

• Point-Slope Form

• Slope-Intercept Form

• There's no additional benefit to either.

Reorder

Convert Ax + By = C to

y = mx + b form.

• Ax + By = C

• Get the y-term by itself.

  (Subtract Ax from both sides.)

  By = -Ax + C

• Get the y variable by itself.

  (Divide both sides by B.)

  y = (-A/B)x + (C/B)

• Check that the equation is in y = mx + b form.

1

2

3

4

• 1
• 2
• 3
• 4

Fill in the Blanks

-4x - 2y = 6

What is the slope?!

Your answer will be a positive or negative integer.

Fill in the Blanks

-4x - 2y = 6

What is the y-intercept?!

Your answer will be a positive or negative integer.

Fill in the Blanks

-3x + 2y = 1

What is the slope?!

Your answer will be a positive or negative fraction.

Fill in the Blanks

-3x + 2y = 1

What is the y-intercept?!

Your answer will be a positive or negative fraction.

Match

Determine the y-intercept for each of the following equations.

Option 1: Use the formula b = C / B.

Option 2: Replace each x with a 0. Then solve for y.

• 2x + 3y = 5

• -3x + 2y = 1

• -4x - 2y = 6

y-intercept: 5/3

y-intercept: 1/2

y-intercept: -3

• y-intercept: 5/3

• y-intercept: 1/2

• y-intercept: -3

Multiple Choice

Which of the following is true about x-intercepts?

• An x-intercept is the x-value when y = 0.

• An x-intercept is the x-value when y = 1.

• x-intercepts always lie on the y-axis.

Match

Determine the x-intercept for each of the following equations.

Hint: Replace each y with a 0. Then solve for x.

• 2x + 3y = 5

• -3x + 2y = 1

• -4x - 2y = 6

x-intercept: 5/2

x-intercept: -1/3

x-intercept: -3/2

• x-intercept: 5/2

• x-intercept: -1/3

• x-intercept: -3/2

Fill in the Blanks

Determine the x-intercept of 4x + 2y = -8.

Remember: Replace y with 0 to find an x-intercept. Then, solve for x.

Fill in the Blanks

Determine the y-intercept of 4x + 2y = -8.

Option 1: Use the formula b = C / B.

Option 2: Replace each x with a 0. Then solve for y.

Graphing

Graph 4x + 2y = -8,

given the y-intercept is -4 and the x-intercept is -2.

Fill in the Blanks

Determine the x-intercept of 3𝑥 − 6𝑦 = 9.

Remember: Replace y with 0 to find an x-intercept. Then, solve for x.

Fill in the Blanks

Determine the y-intercept of 3𝑥 − 6𝑦 = 9.

Option 1: Use the formula b = C / B.

Option 2: Replace x with a 0. Then solve for y.

Your answer will include a decimal. Please do not type a fraction.

Draw

Graph 3𝑥 − 6𝑦 = 9.

Mark that the y-intercept is -1.5 and the x-intercept is 3.

Then, draw a straight line connecting the points.

Multiple Choice

Given an equation in y = # form, like y = 5 or y = -3/4, what kind of line would you see?

• Vertical Line

  (Straight up and down)

• Horizontal Line

• Diagonal Line

• Curve

Multiple Choice

This line is ....

• vertical

• horizontal

• diagonal

• quadratic

Match

Which of the following is a horizontal line? Which is vertical? Which is neither?

• 2𝑥 − 3𝑦 = 12

• 5𝑥 = 4

• y = 3

Neither

Vertical

Horizontal

• Neither

• Vertical

• Horizontal

Graphing

Graph 4x = 8

Hint: Solve for x first.

Graphing

Graph 4𝑥 − 2𝑦 = 8.

Hint: Determine x-intercept. Determine y-intercept.

Plot the intercepts and connect with a line.