Q55. - Algebra 2

Question

The form $\frac{\mathbf{x}}{\mathbf{a}}+\frac{\mathbf{y}}{\mathbf{b}}=\mathbf{1}$ is known as the intercept form of the equation of a line because $\mathbf{a}$ is the $\mathbf{x}$-intercept and $\mathbf{b}$ is the $\mathbf{y}$-intercept.

Write the equation $\mathbf{2}\mathbf{x}-\mathbf{y}-\mathbf{5}=\mathbf{0}$ in the intercept form.

Step-by-Step Solution

Answer

The intercept form of the given equation is $\frac{x}{\left(\frac{5}{2}\right)}+\frac{y}{\left(-5\right)}=1$.

Step 1 – State the concept

Any linear equation of the form $ax+by+c=0$ can be converted to the form $\frac{x}{a}+\frac{y}{b}=1$using suitable algebraic operations.

Step 2 – List the given data

The given equation is $2x-y-5=0$.

Step 3 – Convert to intercept form

$2x-y-5=0$  (Given equation)

 

$2x-y-5+5=0+5$  (Add 5 to both sides)

 

$2x-y=5$   (Simplify)

 

$\frac{2x-y}{5}=\frac{5}{5}$  (Divide both sides by 5)

 

$\frac{2}{5}x-\frac{1}{5}y=1$  (Simplify)

 

$\frac{x}{\left(\frac{5}{2}\right)}+\frac{y}{\left(-5\right)}=1$   (Taking reciprocals of the coefficients)

 

So, $\frac{x}{\left(\frac{5}{2}\right)}+\frac{y}{\left(-5\right)}=1$ is the intercept form of the given equation.