The equation of the line in slope-intercept form is given by
[tex]y=mx+b[/tex]step 1
Find out the slope m
we have the points (-6,5) and (2,1)
[tex]m=\frac{1-5}{2+6}=-\frac{4}{8}=-\frac{1}{2}[/tex]step 2
Find out the equation of the line
we have
m=-1/2
point (2,1)
substitute and solve for b
[tex]\begin{gathered} 1=-\frac{1}{2}(2)+b \\ \\ 1=-1+b \\ b=2 \end{gathered}[/tex]therefore
The equation of the line is
[tex]y=-\frac{1}{2}x+2[/tex]Problem N 2
Write the equation of the line in the point-slope form that passes through the point (-2,3) and has a slope of 1/2
The equation of the line in point-slope form is given by
[tex]y-y_1=m(x-x_1)[/tex]we have
m=1/2
point (-2,3)
substitute
[tex]\begin{gathered} y-3=\frac{1}{2}(x-(-2)) \\ \\ therefore \\ The\text{ answer is} \\ y-3=\frac{1}{2}(x+2) \end{gathered}[/tex]