Question

Express each of the following equations in the form ax + by + c = 0 and indicate the values of a, b, c in each case.
(i) 3x + 5y = 7.5
(ii) $2x-\frac{y}{5}+6=0$
(iii) 3y – 2x = 6
(iv) 4x = 5y
(v) $\frac{x}{5}-\frac{y}{6}=1$
(vi) $\sqrt{2}x+\sqrt{3}y=5$

Answer 1

(i) 3x + 5y = 7.5
This can be expressed in the form ax + by + c = 0 as $3x+5y+\left(-7.5\right)=0$.
(ii) $2x-\frac{y}{5}+6=0$
This can be expressed in the form ax + by + c = 0 as $2x+\left(-\frac{1}{5}\right)y+6=0$
(iii) 3y – 2x = 6
This can be expressed in the form ax + by + c = 0 as $2x+\left(-3y\right)+6=0$.
(iv) 4x = 5y
This can be expressed in the form ax + by + c = 0 as $4x-5y+0=0$
(v) $\frac{x}{5}-\frac{y}{6}=1$
This can be expressed in the form ax + by + c = 0 as $6x-5y=30$
(vi) $\sqrt{2}x+\sqrt{3}y=5$
This can be expressed in the form ax + by + c = 0 as $\sqrt{2}x+\sqrt{3}y+\left(-5\right)=0$