Answer:
[tex]y=-\frac{1}{2}x-3[/tex]
Step-by-step 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: [tex]y-y_{1}=m(x-x_{1})[/tex]
Where,
- [tex](x_{1},y_{1})[/tex] is point 1 and [tex](x_{2},y_{2})[/tex] is point 2
- m is the slope and given by [tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
Using the 2 points given and the formulas shown, we can write:
[tex]y-(-5)=m(x-4)\\y+5=\frac{-3-(-5)}{0-4}(x-4)\\y+5=-\frac{2}{4}(x-4)\\y+5=-\frac{1}{2}(x-4)\\y+5=-\frac{1}{2}x+2\\y=-\frac{1}{2}x+2-5\\y=-\frac{1}{2}x-3[/tex]
Hence, [tex]y=-\frac{1}{2}x-3[/tex] is the equation of the line.
