Answer:
[tex]y=-\frac{5}{3}x-2[/tex]
Step-by-step explanation:
step 1
Convert mixed number to an improper fraction
[tex]-2\frac{1}{4} =-2-\frac{1}{4}=-\frac{9}{4}[/tex]
[tex]1\frac{3}{4} =1+\frac{3}{4}=\frac{7}{4}[/tex]
so
we have the points
[tex](-\frac{9}{4},\frac{7}{4})[/tex] and [tex](-3,3)[/tex]
step 2
Find the slope of the line
The formula to calculate the slope between two points is equal to
[tex]m=\frac{y2-y1}{x2-x1}[/tex]
we have the points
[tex](-\frac{9}{4},\frac{7}{4})[/tex] and [tex](-3,3)[/tex]
substitute
[tex]m=\frac{3-(7/4)}{-3+(9/4)}[/tex]
[tex]m=\frac{5/4}{-3/4}[/tex]
[tex]m=-\frac{5}{3}[/tex]
step 3
Find the equation of the line in point slope form
[tex]y-y1=m(x-x1)[/tex]
we have
[tex]m=-\frac{5}{3}[/tex]
[tex]point\ (-3,3)[/tex]
substitute
[tex]y-3=-\frac{5}{3}(x+3)[/tex]
step 4
Convert to slope intercept form
Isolate the variable y
[tex]y-3=-\frac{5}{3}x-5[/tex]
[tex]y=-\frac{5}{3}x-5+3[/tex]
[tex]y=-\frac{5}{3}x-2[/tex]
