Answer:
[tex]y-6=-\frac{5}{4}(x+2)[/tex]
[tex]y-1=-\frac{5}{4}(x-2)[/tex]
[tex]y-3.5=-1.25x[/tex]
Step-by-step explanation:
step 1
Find the slope of the linear equation
with the points (-2,6) and (2,1)
The formula to calculate the slope between two points is equal to
[tex]m=\frac{y2-y1}{x2-x1}[/tex]
substitute
[tex]m=\frac{1-6}{2+2}[/tex]
[tex]m=-\frac{5}{4}[/tex]
step 2
Find the equation of the line into point slope form
The equation of the line in slope point form is equal to
[tex]y-y1=m(x-x1)[/tex]
we have
[tex]m=-\frac{5}{4}[/tex]
1) with the point (-2,6)
substitute
[tex]y-6=-\frac{5}{4}(x+2)[/tex]
2) with the point (2,1)
substitute
[tex]y-1=-\frac{5}{4}(x-2)[/tex]
3) with the point (0,3.5)
substitute
[tex]y-3.5=-\frac{5}{4}(x-0)[/tex]
[tex]y-3.5=-\frac{5}{4}x[/tex] -------> [tex]y-3.5=-1.25x[/tex]
