Standard Form - Part 1

Presentation

•

Mathematics

•

9th - 12th Grade

•

Practice Problem

•

Hard

Mattison Johnson

Used 5+ times

FREE Resource

3 Slides • 27 Questions

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

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

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.

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.

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.

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.

Fill in the Blanks

-4x - 2y = 6

What is the slope?!

Your answer will be a positive or negative integer.

Type answer...

Fill in the Blanks

-4x - 2y = 6

What is the y-intercept?!

Your answer will be a positive or negative integer.

Type answer...

Fill in the Blanks

-3x + 2y = 1

What is the slope?!

Your answer will be a positive or negative fraction.

Type answer...

Fill in the Blanks

-3x + 2y = 1

What is the y-intercept?!

Your answer will be a positive or negative fraction.

Type answer...

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

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

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.

Type answer...

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.

Type answer...

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.

Type answer...

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.

Type answer...

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

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.

Standard Form

By Mattison Johnson

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