Question

FIFTY POINTS! PLS HELP QUICK!!
the equation of a line that passes through (4,-5) and (0,-3).

Answer 1

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

Explanation:

When 2 points are given, we can use the point slope formula for a line to get the equation.

Point-Slope Form of a line:
`y-y_(1)=m(x-x_(1))`

Where,

• 
  `(x_(1),y_(1))` is point 1 and
  `(x_(2),y_(2))` is point 2
• m is the slope and given by
  `m=(y_(2)-y_(1))/(x_(2)-x_(1))`

Using the 2 points given and the formulas shown, we can write:

`y-(-5)=m(x-4)\\y+5=(-3-(-5))/(0-4)(x-4)\\y+5=-(2)/(4)(x-4)\\y+5=-(1)/(2)(x-4)\\y+5=-(1)/(2)x+2\\y=-(1)/(2)x+2-5\\y=-(1)/(2)x-3`

Hence,
`y=-(1)/(2)x-3` is the equation of the line.