Question

2 express each of the equations in the form ax + by + c = 0.
a) $y = 5x + 3$
b) $y = -3x + 2$
c) $y = \frac{4}{5}x - 2$

Explanation:

Step1: Rearrange equation a)

Subtract $5x$ and $3$ from both sides:
$y - 5x - 3 = 5x + 3 - 5x - 3$
Simplify to get: $-5x + y - 3 = 0$
(Alternatively, multiply by -1: $5x - y + 3 = 0$, both are valid; we use the first result here)

Step2: Rearrange equation b)

Add $3x$ and subtract $2$ from both sides:
$y + 3x - 2 = -3x + 2 + 3x - 2$
Simplify to get: $3x + y - 2 = 0$

Step3: Rearrange equation c)

Multiply all terms by 5 to eliminate fraction:
$5y = 4x - 10$
Subtract $4x$ and add $10$ to both sides:
$5y - 4x + 10 = 4x - 10 - 4x + 10$
Simplify to get: $-4x + 5y + 10 = 0$
(Alternatively, multiply by -1: $4x - 5y - 10 = 0$, both are valid; we use the first result here)

Answer:

a) $-5x + y - 3 = 0$
b) $3x + y - 2 = 0$
c) $-4x + 5y + 10 = 0$

Note: Equivalent forms with all terms multiplied by -1 are also acceptable, e.g., $5x - y + 3 = 0$ for part a)