Answer:
(a) Slope [tex]=\frac{1}{2}[/tex]
(b) [tex](y-9)=\frac{1}{2}(x-8)[/tex]
(c) [tex]y=\frac{x}{2}+5[/tex]
Step-by-step explanation:
(a) slope of line passing through two points [tex](x_1,y_1)[/tex] and [tex](x_{2},y_{2})[/tex] is given by
slope [tex]=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
Here [tex](x_{1},y_{1})=(8,\ 9),\ (x_{2},y_{2})=(-2,\ 4)[/tex]
slope [tex]=\frac{4-9}{-2-8}=\frac{-5}{-10}=\frac{1}{2}[/tex]
Slope [tex]=\frac{1}{2}[/tex]
Equation in point slope form
Equation of line passing through a point [tex](x_{1},\ y_{1})[/tex] and having slope [tex]m[/tex] is given by [tex](y-y_{1})=m(x-\ x_{1})[/tex]
Here [tex](x_{1},y_{1})=(8,9}), \ m=\frac{1}{2}[/tex]
[tex](y-9)=\frac{1}{2}(x-8)[/tex]
slope intercept form
Equation is given by [tex]y=m\ x+b[/tex]
here [tex]m=\frac{1}{2}[/tex]
[tex]y=\frac{x}{2}+b[/tex]
it passes through [tex](8,9)[/tex]
[tex]9=\frac{8}{2}+b\\9=4+b\\b=5[/tex]
Hence equation is [tex]y=\frac{x}{2}+5[/tex]
