Answer:
[tex]2y+x=2[/tex]
Step-by-step explanation:
Given:
Two points are given (−6, 4) and (2, 0).
Write the equation that passes through the given points.
Slope for given points.
[tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
[tex]m=\frac{0-4}{2-(-6)}[/tex]
[tex]m=\frac{-4}{2+6}[/tex]
[tex]m=\frac{-4}{8}[/tex]
[tex]m=\frac{-1}{2}[/tex]
The equation of a line given a point and a slope using the formula
[tex]y-y_{1} =m(x-x_{1} )[/tex]
for point (-6, 4) and slope = m
[tex]y-4 =m(x-(-6))[/tex]
[tex]y-4 =-\frac{1}{2}(x-(-6))[/tex]
[tex]y-4 =-\frac{1}{2}x-\frac{1}{2}\times 6[/tex]
[tex]y+\frac{x}{2} =4-3[/tex]
[tex]\frac{2y+x}{2} =1[/tex]
[tex]2y+x=2[/tex]
The equation of line that passes through the given points is [tex]2y+x=2[/tex].
