Question

Write the equation of the line that satisfies the following conditions:

a. Has a slope of m = − 1
4 and passes through the point (0, −5).
b. Passes through the points (1,3) and (−2, −1).

Answer 1

a.
`y=-x+-5`

b.
`y=(4)/(3)x+(5)/(3)`

Explanation:

to solve part a we have the slope of the line and a point, so we use the point-slope equation

`y=m(x-x_(1))+y_(1)`

where
`m` is the slope:
`m=-1`, and
`(x_(1),y_(1))` is the point, so in this case the point is
`(0,-5)` thus
`x_(1)=0` and
`y_(1)=-5`.Thus the equation is:

`y=-1(x-0)+(-5)`

`y=-x+-5`

And for part b we have two points. With the two points we can find the slope and then use the point-slope equation again.

To find the slope we use:

`m=(y_(2)-y_(1))/(x_(2)-x_(1))`

for the points
`(x_(1),y_(1))` and
`(x_(2),y_(2))`. Since we have the poits:
`(1,3)` and
`(-2,-1)`

`x_(1)=1\\y_(1)=3\\x_(2)=-2\\y_(2)=-1`

Thus, the slope:

`m=(y_(2)-y_(1))/(x_(2)-x_(1))=(-1-3)/(-2-1)`

`m=(-4)/(-3)`

`m=(4)/(3)`

and now using the point-slope equation:

`y=m(x-x_(1))+y_(1)`

`y=(4)/(3)(x-1)+3\\y=(4)/(3)x-(4)/(3) +3\\y=(4)/(3)x+(5)/(3)`