Answer:
[tex]\large\boxed{y=\dfrac{1}{2}x-2}\\\boxed{f(8)=2}\\\boxed{\text{positive}}[/tex]
Step-by-step explanation:
The slope-intercept form of an equation of a line:
[tex]y=mx+b[/tex]
m - slope
b - y-intercept → (0, b)
The fromula of a slope:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
From the graph we hate x-intercept (4, 0) and y-intercept (0, -2) → b = -2
Calculate the slope:
[tex]m=\dfrac{-2-0}{0-4}=\dfrac{-2}{-4}=\dfrac{1}{2}[/tex]
Put the value of te slope and the value of the y-intercept to the equation of a line:
[tex]y=\dfrac{1}{2}x+(-2)=\dfrac{1}{2}x-2[/tex]
Determine f(8).
Put x = 8 to the equation of a line:
[tex]f(8)=\dfrac{1}{2}(8)-2=4-2=2[/tex]
If there is a horizontal shift of 10 to the left, then we have a new line:
[tex]g(x)=f(x+10)[/tex]
[tex]g(x)=\dfrac{1}{2}(x+10)-2[/tex] use the distributive property
[tex]g(x)=\dfrac{1}{2}x+\left(\dfrac{1}{2}\right)(10)-2=\dfrac{1}{2}x+5-2=\dfrac{1}{2}x+3[/tex]
Calculate g(8):
[tex]g(8)=\dfrac{1}{2}(8)+3=4+3=7>0[/tex]
