Answer:
The equation is y = -x + 2.5
Step-by-step explanation:
* Lets explain how to solve the problem
- The form of the equation of a line is y = mx + c , where m is the slope
of the line and c is the y-intercept
- The y-intercept means the line intersect the y-axis at point (0 , c)
- The slope of the line which passes through points (x1 , y1) , (x2 , y2)
is [tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
* Lets solve the problem
∵ The line passes through the points (-8.5 , 11) and (5 , -2.5)
- Let point(x1 , y1) = (-8.5 , 11) and point (x2 , y2) = (5 , -2.5)
∴ x1 = -8.5 , x2 = 5 and y1 = 11 , y2 = -2.5
∴ [tex]m=\frac{-2.5-11}{5-(-8.5)}=\frac{-13.5}{5+8.5}=\frac{-13.5}{13.5}=-1[/tex]
∴ The slope of the line is -1
∵ y = mx + c
∴ y = -x + c
- To find c substitute x and y in the equation by the coordinates of
one of the two points
∵ Point (5 , -2.5) lies on the line
∴ x = 5 at y = -2.5
∵ y = -x + c
∴ -2.5 = -(5) + c
∴ -2.5 = -5 + c
- Add 5 to both sides
∴ c = 2.5
∴ y = -x + 2.5
* The equation is y = -x + 2.5
