Question

1. create a linear function g(x) that is parallel to the function and passes through the given value. f(x) = -\frac{5}{4}x + 3 and f(-8) = 3

Explanation:

Step1: Determine the slope of \( g(x) \)

Parallel lines have the same slope. The function \( f(x) = -\frac{5}{4}x + 3 \) is in slope - intercept form \( y=mx + b \), where \( m \) is the slope. So the slope of \( f(x) \) is \( m = -\frac{5}{4} \), and since \( g(x) \) is parallel to \( f(x) \), the slope of \( g(x) \) is also \( m=-\frac{5}{4} \). Let the equation of \( g(x) \) be \( g(x)=-\frac{5}{4}x + b \).

Step2: Find the value of \( b \)

We know that \( g(- 8)=3 \) (because \( f(-8) = 3 \) and \( g(x) \) passes through the same point as required). Substitute \( x=-8 \) and \( g(x) = 3 \) into the equation \( g(x)=-\frac{5}{4}x + b \):

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Subtract 10 from both sides to solve for \( b \): \( b=3 - 10=-7 \)

Step3: Write the equation of \( g(x) \)

Now that we have the slope \( m = -\frac{5}{4} \) and the y - intercept \( b=-7 \), the equation of the linear function \( g(x) \) is \( g(x)=-\frac{5}{4}x-7 \)

Answer:

\( g(x)=-\frac{5}{4}x - 7 \)