Answer:
[tex]y=-\frac{1}{4} x+1[/tex]
Step-by-step explanation:
Since they give you two points on the lane (-4,2) and (4,0), the line can be determined by using them to find:
1) the slope of the line via the formula:
[tex]slope=\frac{y_2-y_1}{x_2-x_1} =\frac{(0-2)}{4--4} =\frac{-2}{8} =-\frac{1}{4}[/tex]
2) the line's y-intercept (b) requiring that one of the points satisfies the general equation of the line with the slope found above:
[tex]y=m\,x+b\\y=-\frac{1}{4} x+b\\[/tex]
For example using point (4,0) in the equation above:
[tex]y=-\frac{1}{4} x+b\\0=-\frac{1}{4} (4)+b\\0=-1+b\\1=b[/tex]
So the equation of the line through those points in slope intercept form is:
[tex]y=-\frac{1}{4} x+1[/tex]
