Chapter 3.1, Problem 8CYU

To determine

To Graph: The equation $2x-5y=1$ by using x- and y-intercepts.

Explanation of Solution

Given information:

The given equation $2x-5y=1$

Calculation:

To find the x-intercept, let $y=0$

  $\begin{array}{l}2x-5y=1\\ 2x-5\left(0\right)=1\end{array}$

(Replace y by 0)

  $2x=1$

(Simplify)

  $\frac{2x}{2}=\frac{1}{2}$

(Divide both sides by 2)

  $x=\frac{1}{2}$

(Simplify)

Or

  $x=0.5$

The x-intercept is 0.5. This means that the graph intersects the x-axis at $\left(0.5,0\right)$ .

To find the y-intercept, let $x=0$

  $\begin{array}{l}2x-5y=1\\ 2\left(0\right)-5y=1\end{array}$

(Replace x by 0)

  $-5y=1$

(Simplify)

  $\frac{-5y}{5}=\frac{1}{5}$

(Divide 5 on both sides)

  $-y=\frac{1}{5}$

(Simplify)

  $\left(-1\right)\left(-y\right)=\left(-1\right)\frac{1}{5}$

(Multiply by -1 on both sides)

  $y=-\frac{1}{5}$

Or

  $y=-0.2$

(Simplify)

The y-intercept is -0.2. This means the graph intersects the y-axis at $\left(0,-0.2\right)$ .

Plot these two points and then draw a line through them.