Question

algebra
standard form of a linear equation
convert each equation from slope - intercept form to standard form.

1. $y = -\frac{2}{5}x$
2. $y = 2x - 3$ 4) $y = -2x + 1$
3. $y = -6$
4. $y = -3x + 2$ 8) $y=\frac{4}{5}x - 5$

write each equation in standard form. (hint: write in slope - intercept form, then convert to standard form.)

1. slope $=\frac{3}{5}$, y - intercept $= 5$ 10) slope $= 1$, y - intercept $=-3$
2. slope $=-\frac{3}{5}$, y - intercept $=-3$ 12) slope $=\frac{5}{4}$, y - intercept $= 2$

Explanation:

Standard form of a linear equation is $Ax + By = C$, where $A$, $B$, $C$ are integers, and $A\geq0$.

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Problem 3

Step1: Move $2x$ to left side

$y - 2x = -3$

Step2: Rearrange terms, multiply by -1

$-2x + y = -3 \implies 2x - y = 3$

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Problem 4

Step1: Move $-2x$ to left side

$y + 2x = 1$

Step2: Rearrange terms

$2x + y = 1$

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Problem 5

Step1: Rewrite in standard form

$0x + 1y = -6$

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Problem 6

Step1: Move $-x$ to left side

$y + x = -3$

Step2: Rearrange terms

$x + y = -3$

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Problem 7

Step1: Move $-3x$ to left side

$y + 3x = 2$

Step2: Rearrange terms

$3x + y = 2$

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Problem 8

Step1: Move $\frac{4}{5}x$ to left side

$y - \frac{4}{5}x = -5$

Step2: Multiply by 5, rearrange

$-4x + 5y = -25 \implies 4x - 5y = 25$

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Problem 9

Step1: Write slope-intercept form

$y = \frac{3}{5}x + 5$

Step2: Move $\frac{3}{5}x$ to left side

$y - \frac{3}{5}x = 5$

Step3: Multiply by 5, rearrange

$-3x + 5y = 25 \implies 3x - 5y = -25$

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Problem 10

Step1: Write slope-intercept form

$y = 1x - 3$

Step2: Move $x$ to left side

$y - x = -3$

Step3: Rearrange, multiply by -1

$-x + y = -3 \implies x - y = 3$

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Problem 11

Step1: Write slope-intercept form

$y = -\frac{3}{5}x - 3$

Step2: Move $-\frac{3}{5}x$ to left side

$y + \frac{3}{5}x = -3$

Step3: Multiply by 5, rearrange

$3x + 5y = -15$

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Problem 12

Step1: Write slope-intercept form

$y = \frac{5}{4}x + 2$

Step2: Move $\frac{5}{4}x$ to left side

$y - \frac{5}{4}x = 2$

Step3: Multiply by 4, rearrange

$-5x + 4y = 8 \implies 5x - 4y = -8$

Answer:

1. $2x - y = 3$
2. $2x + y = 1$
3. $y = -6$ (or $0x + y = -6$)
4. $x + y = -3$
5. $3x + y = 2$
6. $4x - 5y = 25$
7. $3x - 5y = -25$
8. $x - y = 3$
9. $3x + 5y = -15$
10. $5x - 4y = -8$