Answer:
the equation in the point slope form is
[tex]y-(-2)=-\frac{7}{3} (x-8)[/tex]
and reducing the equation (slope-intercept form)
[tex]y=-\frac{7}{3} x+\frac{50}{3}[/tex]
Step-by-step explanation:
first we calculate the slope of the line with the formula:
[tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
where [tex](x_{1},y_{1})[/tex] is a point where the line passes, and [tex](x_{2},y_{2})[/tex] is another point where the line passes.
Since we have the following points:
(8, -2)
(5,5)
we conclude that
[tex]x_{1}=8\\y_{1}=-2\\x_{2}=5\\y_{2}=5[/tex]
now we substitute this values to find the slope:
[tex]m=\frac{5-(-2)}{5-8}\\ \\m=\frac{5+2}{-3} \\m=-\frac{7}{3}[/tex]
to find the equation now that we know the slope we use the point-slope equation:
[tex]y-y_{1}=m(x-x_{1})[/tex]
and we subtitute the slope and the values of [tex]x_{1}[/tex] and [tex]y_{1}[/tex]:
[tex]y-(-2)=-\frac{7}{3} (x-8)[/tex]
we reduce this equation:
[tex]y+2=-\frac{7}{3} x+\frac{7}{3}*8 \\\\y+2=-\frac{7}{3} x+\frac{56}{3}\\\\y=-\frac{7}{3} x+\frac{56}{3}-2\\ \\y=-\frac{7}{3} x+\frac{50}{3}[/tex]
the equation in the point slope form is
[tex]y-(-2)=-\frac{7}{3} (x-8)[/tex]
and reducing the equation (slope-intercept form)
[tex]y=-\frac{7}{3} x+\frac{50}{3}[/tex]
