Question

Find an equation of the line parallel to −5x+7y=3 that passes through the point (9,−4). If possible, write the equation in slope-intercept form.

Answer 1

From the original equation we have:

`-5x+7y=3`
`7y=5x+3`
`y=(5)/(7)x+(3)/(7)`

The slope of this line is 5/7 and for the new equation to be parallel to the original must have the same slope, and using the point-slope formula we have:

`y-(-4)=(5)/(7)(x-9)`
`y+4=(5)/(7)x-(45)/(7)`
`y=(5)/(7)x-(45)/(7)-4`
`y=(5)/(7)x-(73)/(7)`