Question

32. Select the equation that is correctly displayed in point-slope form:

Answer 1

`y=-(1)/(4)x-(5)/(2)`

Explanation:

Point-Slope Form:
`(y-y_(0))=m(x-x_(0))` where
`(x_(0),y_(0))` is the point our line is passing through and
`m` is the slope of our line.

The question asks us for an equation parallel to
`y=-(1)/(4)x+5`.

We identify that the equation provided is in y-intercept form:
`y=mx+b`

A line parallel to
`y=-(1)/(4)x+5` will have the same slope.

Thus,
`m=-(1)/(4)`.

We were provided the point
`(2,-3)`.

Plugging into our equation for point-slope form:

`(y+3)=-(1)/(4) (x-2)`

This is our answer, however we can simplify this equation into y-intercept form by simply solving for y:

`y=-(1)/(4)x+(2)/(4)-3`

`y=-(1)/(4)x+(1)/(2)-(6)/(2)`

`y=-(1)/(4)x-(5)/(2)`

Thus, the equation parallel to
`y=-(1)/(4)x+5` passing through
`(2,-3)` is:

`y=-(1)/(4)x-(5)/(2)`