Q56. - 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.

56. Identify the $\mathbf{x}$- and $\mathbf{y}$-intercepts of the graph of $\mathbf{2}\mathbf{x}-\mathbf{y}-\mathbf{5}=\mathbf{0}$.

Step-by-Step Solution

Answer

The $x$-intercept of the given equation is $\frac{5}{2}$ and the $y$-intercept of the given equation is $-5$.

Step 1 – State the concept

The graph of $\frac{x}{a}+\frac{y}{b}=1$ has $x$-intercept $a$ and $y$-intercept $b$.

Step 2 – List the given data

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

Step 3 – Determine the intercepts

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

Comparing with $\frac{x}{a}+\frac{y}{b}=1$, $a=\frac{5}{2}$ and $b=-5$.

Thus, the $x$-intercept is $a=\frac{5}{2}$ and $y$-intercept is $b=-5$.