Q. 62 - Precalculus Enhanced with Graphing Utilities

Question

Find an equation for the line with the given properties. Express your answer using either the general form or the slope–intercept form of the equation of a line, whichever you prefer. 

Parallel to the line $x-2y=-5$, containing the point $(0,0)$

Step-by-Step Solution

Answer

The equation of line is $y=\frac{1}{2}x$

Step 1. Given Information

The given point is $(0,0)$ and the equation of parallel line is $x-2y=-5$

Step 2. Calculation

Convert the given line in point-slope form. 

$$\begin{gathered} x-2y=-5 \\ x-x-2y=-x-5 \\ -2y=-x-5 \\ y=\frac{1}{2}x+\frac{5}{2} \end{gathered}$$

Thus, the slope of line is $\frac{1}{2}$

Substitute the given values in the equation of point-slope form.

$$\begin{gathered} y-y_1=m(x-x_1) \\ y-0=\frac{1}{2}(x-0) \\ y=\frac{1}{2}x \end{gathered}$$