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$(0,0)$

Short answer

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

Step-by-step solution

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.

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