Answer:
The linear function is [tex]h = -2\cdot x + 4[/tex]. [tex]h(7) = -10[/tex]
Step-by-step explanation:
Any linear function is represented by a first-order polynomial, whose form is:
[tex]h = m\cdot x + b[/tex]
Where:
[tex]h[/tex] - Independent variable, dimensionless.
[tex]y[/tex] - Dependent variable, dimensionless.
[tex]m[/tex] - Slope, dimensionless.
[tex]b[/tex] - y-Intercept, dimensionless.
From Analytical Geometry we know that slope can be obtained from two distinct points lying on the linear function:
[tex]m = \frac{h_{2}-h_{1}}{x_{2}-x_{1}}[/tex]
If we know that [tex]x_{1} = -1[/tex], [tex]h_{1} = 6[/tex], [tex]x_{2} = 8[/tex] and [tex]h_{2} = -12[/tex], then the slope is:
[tex]m = \frac{-12-6}{8-(-1)}[/tex]
[tex]m = -2[/tex]
Now, we determine the y-intercept in linear function formula: ([tex]m = -2[/tex], [tex]x= 8[/tex] and [tex]h = -12[/tex])
[tex]-12 = -2\cdot (8)+b[/tex]
[tex]-12 = -16 + b[/tex]
[tex]b = 4[/tex]
The linear function is [tex]h = -2\cdot x + 4[/tex]. Finally, we evaluate the expression at [tex]x = 7[/tex]:
[tex]h (7) = -2\cdot (7) + 4[/tex]
[tex]h(7) = -10[/tex]
