Question

Need help! a.s.a.p! please!

Answer 1

Answer:

$\large\boxed{y=\dfrac{1}{2}x-2}\\\boxed{f(8)=2}\\\boxed{\text{positive}}$

Step-by-step explanation:

The slope-intercept form of an equation of a line:

$y=mx+b$

m - slope

b - y-intercept → (0, b)

The fromula of a slope:

$m=\dfrac{y_2-y_1}{x_2-x_1}$

From the graph we hate x-intercept (4, 0) and y-intercept (0, -2) → b = -2

Calculate the slope:

$m=\dfrac{-2-0}{0-4}=\dfrac{-2}{-4}=\dfrac{1}{2}$

Put the value of te slope and the value of the y-intercept to the equation of a line:

$y=\dfrac{1}{2}x+(-2)=\dfrac{1}{2}x-2$

Determine f(8).

Put x = 8 to the equation of a line:

$f(8)=\dfrac{1}{2}(8)-2=4-2=2$

If there is a horizontal shift of 10 to the left, then we have a new line:

$g(x)=f(x+10)$

$g(x)=\dfrac{1}{2}(x+10)-2$          use the distributive property

$g(x)=\dfrac{1}{2}x+\left(\dfrac{1}{2}\right)(10)-2=\dfrac{1}{2}x+5-2=\dfrac{1}{2}x+3$

Calculate g(8):

$g(8)=\dfrac{1}{2}(8)+3=4+3=7>0$