Answer:
[tex]y = 1\frac{1}{4}x+7[/tex]
Step-by-step explanation:
The equation of a straight line can be written as [tex]y=mx+b[/tex].
With the pair of coordinates (coordinates are written in the form [tex](x,y)[/tex] ) , the following can be written:
[tex]2=-4m+b[/tex]
[tex]-3=-8m+b[/tex]
To solve for a variable, we can use elimination:
[tex]-4m+b-(-8m+b)=2-(-3)[/tex] (subtract the second equation from the first)
[tex]-4m+b+8m-b=2+3[/tex]
[tex]4m=5[/tex] ([tex]b[/tex] is eliminated)
[tex]m=\frac{5}{4}[/tex]
[tex]=1\frac{1}{4}[/tex]
To solve for the other variable, we can use substitution:
[tex]2=-4m+b[/tex]
[tex]2=-4(1\frac{1}{4})+b[/tex]
[tex]2 = -5 + b[/tex]
[tex]b = 7[/tex]
[tex]\therefore y=1\frac{1}{4}x+7[/tex] is the linear equation for the line that passes through the points [tex](-4, 2)[/tex] and [tex](-8,-3)[/tex]
