91Ó°ÊÓ

The equation of the given line is $2x+3y=6$and the given point is $(0,5)$.

We will make use of the fact that parallel lines have the same slope to solve this problem.

• The slope-intercept form of the equation of a line is $y=mx+b$where $m$is the slope and$b$ is the y-intercept.
• The slope-point form of an equation of a line with the slope$m$ and the point$\left(x_1,y_1\right)$ is$y-y_1=m(x-x_1)$

The equation of the given line is $2x+3y=6$

To find the slope of this equation, we will rewrite this in the slope-intercept form,

$$\begin{gathered} 2x+3y=6 \\ 3y=-2x+6 \\ y=-\frac{2}{3}x+\frac{6}{3} \\ y=-\frac{2}{3}x+2 \end{gathered}$$

Therefore the slope of the given line is $-\frac{2}{3}$

As the parallel lines have the same slope, we can say that the line which is parallel to the line hasthe slope$-\frac{2}{3}$as well.

The slope of the parallel line is $-\frac{2}{3}$and the point on that line is $(0,5)$

Then using the slope-point formula, we have

$$\begin{gathered} y-y_1=m(x-x_1) \\ y-5=-\frac{2}{3}(x-0) \\ y=-\frac{2}{3}x+5 \end{gathered}$$

Therefore the equation of the parallel line in the slope-intercept form is$y=-\frac{2}{3}x+5$