Answer:
y=-5x+1
Step-by-step explanation:
y-y1=m(x-x1)
y-(-9)=-5(x-2)
y+9=-5x+10
y=-5x+10-9
y=-5x+1
The linear equation that passes through the point (2,-9) and has a slope of -5 is [tex]\rm\bold{ y = -5x +1}[/tex]
The equation of line passing through a point [tex]\rm (x_1,y_1)[/tex] and having slope [tex]m[/tex] is written as
[tex]\rm\bold{ {y} = mx +c}[/tex]
where [tex]\rm m[/tex] is slope of line
[tex]\rm c[/tex] is y intercept.
So According to the given condition
Slope of the line = -5
Since the slope is negative so the angle subtended by line at x axis in counterclockwise direction is more than 90°.
Also the line passes through (2,-9) and hence point (2,-9) satisfies the standard equation of line and hence we can write that
-9 = (-5) (2) + c
Solving for c we get
-9 + 10 = c
c =1
So the equation of line becomes
[tex]\rm y = -5x +1[/tex]
For more information please refer to the link below
https://brainly.com/question/20632687
