Question

write each equation in standard form using integers.

1. $y = 3x + 1$ 8) $y = 4x - 7$ 9) $y = \frac{1}{2}x - 3$
2. $y = \frac{2}{3}x + 5$ 11) $y = -\frac{3}{4}x - 4$ 12) $y = -\frac{4}{5}x - 7$
3. $y = \frac{7}{2}x + \frac{1}{4}$ 14) $y = -\frac{2}{5}x + \frac{1}{10}$ 15) $y = -3x$
4. write an equation of a line (in standard form) that has the same slope as the line $3x - 5y = 7$ and the same y - intercept as the line $2y - 9x = 8$.

Explanation:

7) Step1: Rearrange to standard form

Standard form: $Ax + By = C$. Subtract $3x$ from both sides.
$y - 3x = 1$ → $-3x + y = 1$ (or multiply by -1: $3x - y = -1$)

8) Step1: Rearrange to standard form

Subtract $4x$ from both sides.
$y - 4x = -7$ → $-4x + y = -7$ (or multiply by -1: $4x - y = 7$)

9) Step1: Eliminate fraction, multiply by 2

$2y = x - 6$

9) Step2: Rearrange to standard form

Subtract $x$ from both sides.
$-x + 2y = -6$ (or multiply by -1: $x - 2y = 6$)

10) Step1: Eliminate fraction, multiply by 3

$3y = 2x + 15$

10) Step2: Rearrange to standard form

Subtract $2x$ from both sides.
$-2x + 3y = 15$ (or multiply by -1: $2x - 3y = -15$)

11) Step1: Eliminate fraction, multiply by 4

$4y = -3x - 16$

11) Step2: Rearrange to standard form

Add $3x$ to both sides.
$3x + 4y = -16$

12) Step1: Eliminate fraction, multiply by 5

$5y = -4x - 35$

12) Step2: Rearrange to standard form

Add $4x$ to both sides.
$4x + 5y = -35$

13) Step1: Eliminate fractions, multiply by 4

$4y = 14x + 1$

13) Step2: Rearrange to standard form

Subtract $14x$ from both sides.
$-14x + 4y = 1$ (or multiply by -1: $14x - 4y = -1$)

14) Step1: Eliminate fractions, multiply by 10

$10y = -4x + 1$

14) Step2: Rearrange to standard form

Add $4x$ to both sides.
$4x + 10y = 1$

15) Step1: Rearrange to standard form

Add $3x$ to both sides.
$3x + y = 0$

16) Step1: Find slope of $3x-5y=7$

Rewrite in slope-intercept: $-5y = -3x +7$ → $y=\frac{3}{5}x-\frac{7}{5}$. Slope $m=\frac{3}{5}$

16) Step2: Find y-intercept of $2y-9x=8$

Rewrite in slope-intercept: $2y=9x+8$ → $y=\frac{9}{2}x+4$. Y-intercept $b=4$

16) Step3: Write slope-intercept equation

$y=\frac{3}{5}x+4$

16) Step4: Convert to standard form

Multiply by 5: $5y=3x+20$, rearrange to $-3x+5y=20$ (or $3x-5y=-20$)

Answer:

1. $3x - y = -1$ (or $-3x + y = 1$)
2. $4x - y = 7$ (or $-4x + y = -7$)
3. $x - 2y = 6$ (or $-x + 2y = -6$)
4. $2x - 3y = -15$ (or $-2x + 3y = 15$)
5. $3x + 4y = -16$
6. $4x + 5y = -35$
7. $14x - 4y = -1$ (or $-14x + 4y = 1$)
8. $4x + 10y = 1$
9. $3x + y = 0$
10. $3x - 5y = -20$ (or $-3x + 5y = 20$)