Question

Determine the equation of the line that passes through the point (1/9,7) and is parallel to the line −10y+6x=6.

Answer 1

Parallel lines have the same slope. Therefore, we need to first find the slope in the first equation converting the equation in the slope-intercept form so we can determine the equation of the line that passes through the poin(1/9, 7):

`\begin{gathered} Slope\text{ intercept form: y=mx +b} \\ \text{ -10y + 6x=6 } \\ \text{ -10y= -6x + 6} \\ y=\text{ }(-6x)/(10)\text{ +}(6)/(10) \\ y=\text{ -}(3)/(5)x\text{ + }(3)/(5) \\ \\ The\text{ slope here is -}(3)/(5) \\ \\ Now\text{ that we know we can replace the point in the slope-intercept equation:} \\ y=\text{ mx + b} \\ 7=\text{ -}(3)/(5)((1)/(9))\text{ + b} \\ 7=\text{ - }(3)/(45)\text{ + b} \\ 7=\text{ -}(1)/(15)\text{ + b} \\ 7\text{ + }(1)/(15)=\text{ b} \\ \frac{105\text{ + 1}}{15}=\text{ b} \\ (106)/(15)=b \\ \\ Therefore\text{ the equation of the line is:} \\ y=\text{ -}(3)/(5)x\text{ + }(106)/(15) \end{gathered}`