Answer:
[tex]h(1) =\frac{29}{3}[/tex] or [tex]h(1) =9.67[/tex]
Step-by-step explanation:
h(5) = - 7 --> (5, 7)
h( - 1) = 11 --> (-1, 11)
Using those two points to find the slope:
Slope (m) = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]m =\frac{11-7}{(-1)-5}[/tex]
[tex]m =\frac{4}{-6}[/tex]
[tex]m =-\frac{2}{3}[/tex]
[tex](5, 7)[/tex]
[tex]y = mx + b[/tex]
[tex]y=-\frac{2}{3}x+b[/tex]
[tex]7=-\frac{2}{3}(5)+b[/tex]
[tex]7=-\frac{10}{3}+b[/tex]
[tex]3(7=-\frac{10}{3}+b)[/tex]
[tex]21=-10+3b[/tex]
[tex]+10[/tex] [tex]+10[/tex]
[tex]31=3b[/tex]
[tex]/3[/tex] [tex]/3[/tex]
[tex]\frac{31}{3} =b[/tex]
[tex]y=-\frac{2}{3}x+\frac{31}{3}[/tex]
[tex]h(1) =-\frac{2}{3}(1)+\frac{31}{3}[/tex]
[tex]h(1) =-\frac{2}{3}+\frac{31}{3}[/tex]
[tex]h(1) =\frac{29}{3}[/tex]
[tex]h(1) =9.67[/tex]
Hope this helps!
