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Find a linear function h, given h(5) = - 7 and h( - 1) = 11. Then find h(1).

Sagot :

Esther

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!

View image Esther
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