Math / Algebra

QuestionAlgebra 1 Lesson 4.1 Day 2 Assignment Slope Intercept back to Standard Form Name/Period Remember that for a line to be in Standard Form, $A x+B y=C$ , the following must be true: 1. 2. 3.
Take the slope intercept form of each equation, and write the equation in Standard Form.
1. $\mathrm{y}=2 \mathrm{x}+4$
2. $y=3 x-4$
3. $y=\frac{1}{2} x+4$
4. $y=\frac{2}{3} x-1$
5. $y=-\frac{3}{4} x+2$
6. $y=-\frac{1}{4} x-5$

Studdy Solution

STEP 1

1. We are given equations in slope-intercept form, $y = mx + b$ .
2. We need to convert these equations into standard form, $Ax + By = C$ .
3. The standard form requires: - $A, B,$ and $C$ are integers. - $A$ should be non-negative. - $A, B,$ and $C$ should have no common factors other than 1.

STEP 2

1. Rearrange each equation to move the $x$ -term to the left side.
2. Ensure all coefficients are integers.
3. Adjust the equation to meet the standard form criteria.

STEP 3

Convert the equation $y = 2x + 4$ to standard form:
Rearrange to get $-2x + y = 4$ .
Multiply through by $-1$ to make $A$ positive:
$2x - y = -4$

STEP 4

Convert the equation $y = 3x - 4$ to standard form:
Rearrange to get $-3x + y = -4$ .
Multiply through by $-1$ to make $A$ positive:
$3x - y = 4$

STEP 5

Convert the equation $y = \frac{1}{2}x + 4$ to standard form:
Rearrange to get $-\frac{1}{2}x + y = 4$ .
Multiply through by 2 to clear the fraction:
$-x + 2y = 8$
Multiply through by $-1$ to make $A$ positive:
$x - 2y = -8$

STEP 6

Convert the equation $y = \frac{2}{3}x - 1$ to standard form:
Rearrange to get $-\frac{2}{3}x + y = -1$ .
Multiply through by 3 to clear the fraction:
$-2x + 3y = -3$
Multiply through by $-1$ to make $A$ positive:
$2x - 3y = 3$

STEP 7

Convert the equation $y = -\frac{3}{4}x + 2$ to standard form:
Rearrange to get $\frac{3}{4}x + y = 2$ .
Multiply through by 4 to clear the fraction:
$3x + 4y = 8$

STEP 8

Convert the equation $y = -\frac{1}{4}x - 5$ to standard form:
Rearrange to get $\frac{1}{4}x + y = -5$ .
Multiply through by 4 to clear the fraction:
$x + 4y = -20$

Was this helpful?

Studdy Solution

STEP 1

1. We are given equations in slope-intercept form, $y = mx + b$ .
2. We need to convert these equations into standard form, $Ax + By = C$ .
3. The standard form requires: - $A, B,$ and $C$ are integers. - $A$ should be non-negative. - $A, B,$ and $C$ should have no common factors other than 1.

STEP 2

1. Rearrange each equation to move the $x$ -term to the left side.
2. Ensure all coefficients are integers.
3. Adjust the equation to meet the standard form criteria.

STEP 3

Convert the equation $y = 2x + 4$ to standard form:
Rearrange to get $-2x + y = 4$ .
Multiply through by $-1$ to make $A$ positive:
$2x - y = -4$

STEP 4

Convert the equation $y = 3x - 4$ to standard form:
Rearrange to get $-3x + y = -4$ .
Multiply through by $-1$ to make $A$ positive:
$3x - y = 4$

STEP 5

Convert the equation $y = \frac{1}{2}x + 4$ to standard form:
Rearrange to get $-\frac{1}{2}x + y = 4$ .
Multiply through by 2 to clear the fraction:
$-x + 2y = 8$
Multiply through by $-1$ to make $A$ positive:
$x - 2y = -8$

STEP 6

Convert the equation $y = \frac{2}{3}x - 1$ to standard form:
Rearrange to get $-\frac{2}{3}x + y = -1$ .
Multiply through by 3 to clear the fraction:
$-2x + 3y = -3$
Multiply through by $-1$ to make $A$ positive:
$2x - 3y = 3$

STEP 7

Convert the equation $y = -\frac{3}{4}x + 2$ to standard form:
Rearrange to get $\frac{3}{4}x + y = 2$ .
Multiply through by 4 to clear the fraction:
$3x + 4y = 8$

STEP 8

Convert the equation $y = -\frac{1}{4}x - 5$ to standard form:
Rearrange to get $\frac{1}{4}x + y = -5$ .
Multiply through by 4 to clear the fraction:
$x + 4y = -20$

Get Studdy

Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Studdy Solution

STEP 1

STEP 2

1. Rearrange each equation to move the x x x-term to the left side.2. Ensure all coefficients are integers.3. Adjust the equation to meet the standard form criteria.

STEP 3

Convert the equation y=2x+4 y = 2x + 4 y=2x+4 to standard form:Rearrange to get −2x+y=4 -2x + y = 4 −2x+y=4.Multiply through by −1-1−1 to make A A A positive:2x−y=−4 2x - y = -4 2x−y=−4

STEP 4

Convert the equation y=3x−4 y = 3x - 4 y=3x−4 to standard form:Rearrange to get −3x+y=−4 -3x + y = -4 −3x+y=−4.Multiply through by −1-1−1 to make A A A positive:3x−y=4 3x - y = 4 3x−y=4

STEP 5

STEP 6

STEP 7

Convert the equation y=−34x+2 y = -\frac{3}{4}x + 2 y=−43​x+2 to standard form:Rearrange to get 34x+y=2 \frac{3}{4}x + y = 2 43​x+y=2.Multiply through by 4 to clear the fraction:3x+4y=8 3x + 4y = 8 3x+4y=8

STEP 8

Convert the equation y=−14x−5 y = -\frac{1}{4}x - 5 y=−41​x−5 to standard form:Rearrange to get 14x+y=−5 \frac{1}{4}x + y = -5 41​x+y=−5.Multiply through by 4 to clear the fraction:x+4y=−20 x + 4y = -20 x+4y=−20

Get Studdy

Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

1. Rearrange each equation to move the $x$ -term to the left side.
2. Ensure all coefficients are integers.
3. Adjust the equation to meet the standard form criteria.

Convert the equation $y = 2x + 4$ to standard form:
Rearrange to get $-2x + y = 4$ .
Multiply through by $-1$ to make $A$ positive:
$2x - y = -4$

Convert the equation $y = 3x - 4$ to standard form:
Rearrange to get $-3x + y = -4$ .
Multiply through by $-1$ to make $A$ positive:
$3x - y = 4$

Convert the equation $y = -\frac{3}{4}x + 2$ to standard form:
Rearrange to get $\frac{3}{4}x + y = 2$ .
Multiply through by 4 to clear the fraction:
$3x + 4y = 8$

Convert the equation $y = -\frac{1}{4}x - 5$ to standard form:
Rearrange to get $\frac{1}{4}x + y = -5$ .
Multiply through by 4 to clear the fraction:
$x + 4y = -20$