Question

write the equation of the line parallel to $f(x)=-\frac{3}{8}x + 7$ that passes through the point $(5,9)$
$y - 9=\frac{8}{3}(x - 5)$
$y + 5=\frac{8}{3}(x + 9)$
$y - 9=-\frac{3}{8}(x - 5)$
$y + 9=\frac{8}{3}(x + 5)$
question 19 (4 points)
an electric board determines its monthly bills for residential customers by charging a base price of $25 plus an energy charge of $0.13 per kilowatt - hour (kwh) used. write an equation for the monthly charge $y$ (in dollars) as a function of $x$, the number of kwh used.
$y = 25x+0.13$
$y = 25.13x$
$y = 0.13x + 25$
$y = 25.13$

Explanation:

First Problem

Step1: Identify parallel line slope

Parallel lines have equal slopes. The slope of $f(x)=-\frac{3}{8}x+7$ is $m=-\frac{3}{8}$.

Step2: Use point-slope form

Point-slope formula: $y-y_1=m(x-x_1)$. Substitute $(x_1,y_1)=(5,9)$ and $m=-\frac{3}{8}$.
<Expression>
$y-9=-\frac{3}{8}(x-5)$
</Expression>

Step1: Define fixed and variable costs

Fixed base price: $\$25$. Variable cost: $\$0.13$ per kWh ($x$).

Step2: Build total cost function

Total cost $y$ = variable cost + fixed cost.
<Expression>
$y=0.13x+25$
</Expression>

Answer:

$y - 9 = -\frac{3}{8}(x - 5)$

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Second Problem