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3 years ago

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A proportional relationship between the number of pounds of potatoes (x) and the price in dollars (y) is graphed, and the ordere

d pair (4, 3) is on the graphed line.
Part A: What is the price of 1 pound of potatoes? Show your work, including the proportion you used to determine the price. (8 points)
Part B: What does the ordered pair (8, 6) on the graph represent? Explain in words. (2 points)

1 answer:

Ronch [10]3 years ago

8 0

Part A

We have x = 4 and y = 3 paired up together.

This says that 4 pounds of potatoes cost $3

The price per pound (aka unit price) is y/x = 3/4 = 0.75 dollars = 75 cents.

Answer: 75 cents per pound

========================================

Part B

The ordered pair (8,6) means x = 8 and y = 6 pair up together.

So in this case, 8 pounds of potatoes cost $6.

notice how y/x = 6/8 = 3/4 = 0.75 dollars = 75 cents here as well. So we get the same unit cost.

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$\Large\boxed{\text{Perpendicular Equation:} \ y = -\frac{2}{7}x + \frac{22}{7}}$

$\Large\boxed{\text{Parallel Equation:} \ y = \frac{7}{2}x -12}$

Step-by-step explanation:

In order to find the equations that are parallel/perpendicular to the line $y = \frac{7}{2}x - 4$ , we need to note a couple things about the relationships between lines and their parallel/perpendicular lines.

A) If a line is perpendicular to another, the slopes will be opposite reciprocals (for instance $-2$ and $\frac{1}{2}$ - multiplied, they equal -1.)
B) If a line is parallel to another, they will have the exact same slope.

<h2>Perpendicular:</h2>

We know that the slope of a perpendicular line will be the the opposite reciprocal of the line we're comparing it to.

Since the slope of our base line is $\frac{7}{2}$ , we can find the reciprocal, then the opposite of that.

Reciprocal of $\frac{7}{2} = \frac{2}{7}$
Opposite of $\frac{2}{7} = -\frac{2}{7}$

So the slope of this line will be $-\frac{2}{7}$ , making our equation $y = -\frac{2}{7}x+ b$

However, y-intercepts will not stay the same. In order to find this, we can substitute the point (4, 2) into our equation to solve for b.

$2 = -\frac{2}{7} \cdot 4 + b$
$2 = -\frac{8}{7} + b$
$b = 2+\frac{8}{7}$
$b = 2 \frac{8}{7}$
$b=\frac{22}{7}$

Now we know the y-intercept of this equation is $\frac{22}{7}$ . We can now finish off our equation of the line by substituting that in to what we already have, $y = -\frac{2}{7}x+ b$ .

$y = -\frac{2}{7}x+ \frac{22}{7}$

<h2>Parallel:</h2>

As mentioned earlier, parallel lines will have the exact same slope but not the same y-intercept. Since the slope of our original equation is $\frac{7}{2}$ , the slope for this one will also be $\frac{7}{2}$ .

So we now know the equation looks something like $y = \frac{7}{2}x + b$ .

In order to solve for b, we apply the same logic we did in the perpendicular line and substitute in the point (4, 2) into the equation.

$2 = \frac{7}{2} \cdot 4 + b$
$2 = \frac{28}{2}+b$
$2 = 14+b$
$b = 2-14$

$b =-12$

Now that we know the slope and the y-intercept, we can finish off our equation as $y = \frac{7}{2}x -12$ .

Hope this helped!

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