Question

Find the equation of the line through point (8, -9) that is parallel to the line with slope -5/18

Answer 1

`y=-(5)/(18)x-(61)/(9)`

Step-by-step explanation

The equation of the line can be given by the slope-intercept form:

`y=mx+b`

where m is the slope and b is the y-intercept.

Additionally, parallel lines have the same slope, meaning that if the slope of the parallel line (to our line) is -5/18, then our slope is also -5/18, leaving us with the line:

`y=-(5)/(18)x+b`

Next, we have to replace the values of the point (8, -9) given to:

`-9=-(5)/(18)\cdot8+b`
`-9=-(20)/(9)+b`
`-9+(20)/(9)=b`
`b=-9+(20)/(9)`
`b=-(61)/(9)`

Finally, by rearranging the equation we get:

`y=-(5)/(18)x-(61)/(9)`