Question

example 4) solve $-\frac{1}{3}(-x + 9)=\frac{2}{3}x - 2$ by graphing.
equation 1:
the $y$-intercept is
the slope is
equation 2:
the $y$-intercept is
the slope is
answer:
example 5) there are two towing companies in your neighborhood. each company’s price is described below.

• auto shop towing: $15 pickup fee and $0.50 for every mile.
• benny’s towing service: $10 pickup fee and $0.75 for every hour.

equation 1:
the $y$-intercept is
the slope is
equation 2:
the $y$-intercept is
the slope is
after how many miles is the price the same at both towing companies?

Explanation:

Example 4

Step1: Simplify left equation

$y = -\frac{1}{3}(-x+9) = \frac{1}{3}x - 3$

Step2: Identify Equation 1 values

y-intercept: $-3$, slope: $\frac{1}{3}$

Step3: Define right equation

$y = \frac{2}{3}x - 2$

Step4: Identify Equation 2 values

y-intercept: $-2$, slope: $\frac{2}{3}$

Step5: Set equations equal

$\frac{1}{3}x - 3 = \frac{2}{3}x - 2$

Step6: Solve for x

$-3 + 2 = \frac{2}{3}x - \frac{1}{3}x$
$-1 = \frac{1}{3}x$
$x=5$

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Example 5

Step1: Write Auto Shop equation

Let $y$ = total cost, $x$ = miles.
$y = 0.50x + 15$

Step2: Identify Equation 1 values

y-intercept: $15$, slope: $0.50$

Step3: Write Benny's equation

$y = 0.75x + 10$

Step4: Identify Equation 2 values

y-intercept: $10$, slope: $0.75$

Step5: Set costs equal

$0.50x + 15 = 0.75x + 10$

Step6: Solve for x

$15 - 10 = 0.75x - 0.50x$
$5 = 0.25x$
$x=20$

Answer:

$x=5$