Math / Algebra

QuestionThe line $y-14=6(x-2.5)$ represents Barry's profit, $y$ , from selling $x$ paintings, after buying some canvas. What was the cost of the canvas? \$

Studdy Solution

STEP 1

What is this asking? How much did Barry spend on canvas before selling any paintings? Watch out! Don't mix up the number of paintings sold ( $x$ ) with the profit ( $y$ ).

STEP 2

1. Rewrite the equation
2. Calculate the cost of the canvas

STEP 3

Alright, let's rewrite this equation in a more familiar form.
We've got $y - 14 = 6(x - 2.5)$ , which is Barry's profit equation.
Remember, $y$ is the profit, and $x$ is the number of paintings sold.

STEP 4

Let's distribute that $6$ on the right side.
We do this by multiplying $6$ by both terms inside the parentheses.
Why? Because each painting contributes to the profit!
So, we get $y - 14 = 6 \cdot x - 6 \cdot 2.5$ , which simplifies to $y - 14 = 6x - 15$ .

STEP 5

Now, let's isolate $y$ by adding $14$ to both sides of the equation.
We're doing this to get the profit equation in slope-intercept form, which is super useful!
This gives us $y - 14 + 14 = 6x - 15 + 14$ , which simplifies to $y = 6x - 1$ .

STEP 6

Think about what happens when Barry hasn't sold any paintings yet.
That means $x = 0$ .
Substituting $x = 0$ into our profit equation, $y = 6x - 1$ , we get $y = 6 \cdot 0 - 1$ .

STEP 7

This simplifies to $y = -1$ .
Remember, $y$ represents Barry's profit.
So, a profit of $-1$ means Barry has lost $\$1$ .
This loss represents the cost of the canvas because he hasn't made any money from selling paintings yet.

STEP 8

Therefore, the cost of the canvas was $\$1$ .

STEP 9

The cost of the canvas was $\$1$ .

Was this helpful?

QuestionThe line $y-14=6(x-2.5)$ represents Barry's profit, $y$ , from selling $x$ paintings, after buying some canvas. What was the cost of the canvas? \$

Studdy Solution

STEP 1

What is this asking? How much did Barry spend on canvas before selling any paintings? Watch out! Don't mix up the number of paintings sold ( $x$ ) with the profit ( $y$ ).

STEP 2

1. Rewrite the equation
2. Calculate the cost of the canvas

STEP 3

Alright, let's rewrite this equation in a more familiar form.
We've got $y - 14 = 6(x - 2.5)$ , which is Barry's profit equation.
Remember, $y$ is the profit, and $x$ is the number of paintings sold.

STEP 4

Let's distribute that $6$ on the right side.
We do this by multiplying $6$ by both terms inside the parentheses.
Why? Because each painting contributes to the profit!
So, we get $y - 14 = 6 \cdot x - 6 \cdot 2.5$ , which simplifies to $y - 14 = 6x - 15$ .

STEP 5

Now, let's isolate $y$ by adding $14$ to both sides of the equation.
We're doing this to get the profit equation in slope-intercept form, which is super useful!
This gives us $y - 14 + 14 = 6x - 15 + 14$ , which simplifies to $y = 6x - 1$ .

STEP 6

Think about what happens when Barry hasn't sold any paintings yet.
That means $x = 0$ .
Substituting $x = 0$ into our profit equation, $y = 6x - 1$ , we get $y = 6 \cdot 0 - 1$ .

STEP 7

This simplifies to $y = -1$ .
Remember, $y$ represents Barry's profit.
So, a profit of $-1$ means Barry has lost $\$1$ .
This loss represents the cost of the canvas because he hasn't made any money from selling paintings yet.

STEP 8

Therefore, the cost of the canvas was $\$1$ .

STEP 9

The cost of the canvas was $\$1$ .

Get Studdy

Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

QuestionThe line y−14=6(x−2.5)y-14=6(x-2.5)y−14=6(x−2.5) represents Barry's profit, yyy, from selling xxx paintings, after buying some canvas. What was the cost of the canvas? \$

Studdy Solution

STEP 1

What is this asking? How much did Barry spend on canvas before selling any paintings? Watch out! Don't mix up the number of paintings sold (xxx) with the profit (yyy).

STEP 2

1. Rewrite the equation2. Calculate the cost of the canvas

STEP 3

Alright, let's **rewrite** this equation in a more familiar form.We've got y−14=6(x−2.5)y - 14 = 6(x - 2.5)y−14=6(x−2.5), which is Barry's **profit** equation.Remember, yyy is the **profit**, and xxx is the **number of paintings** sold.

STEP 4

STEP 5

Now, let's **isolate** yyy by adding 141414 to both sides of the equation.We're doing this to get the profit equation in **slope-intercept form**, which is super useful!This gives us y−14+14=6x−15+14y - 14 + 14 = 6x - 15 + 14y−14+14=6x−15+14, which simplifies to y=6x−1y = 6x - 1y=6x−1.

STEP 6

Think about what happens when Barry hasn't sold any paintings yet.That means x=0x = 0x=0.Substituting x=0x = 0x=0 into our **profit** equation, y=6x−1y = 6x - 1y=6x−1, we get y=6⋅0−1y = 6 \cdot 0 - 1y=6⋅0−1.

STEP 7

This simplifies to y=−1y = -1y=−1.Remember, yyy represents Barry's **profit**.So, a profit of −1-1−1 means Barry has lost $1\$1$1.This loss represents the **cost of the canvas** because he hasn't made any money from selling paintings yet.

STEP 8

Therefore, the cost of the canvas was $1\$1$1.

STEP 9

The cost of the canvas was $1\$1$1.

Get Studdy

Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

QuestionThe line $y-14=6(x-2.5)$ represents Barry's profit, $y$ , from selling $x$ paintings, after buying some canvas. What was the cost of the canvas? \$

What is this asking? How much did Barry spend on canvas before selling any paintings? Watch out! Don't mix up the number of paintings sold ( $x$ ) with the profit ( $y$ ).

1. Rewrite the equation
2. Calculate the cost of the canvas

Alright, let's rewrite this equation in a more familiar form.
We've got $y - 14 = 6(x - 2.5)$ , which is Barry's profit equation.
Remember, $y$ is the profit, and $x$ is the number of paintings sold.

Now, let's isolate $y$ by adding $14$ to both sides of the equation.
We're doing this to get the profit equation in slope-intercept form, which is super useful!
This gives us $y - 14 + 14 = 6x - 15 + 14$ , which simplifies to $y = 6x - 1$ .

Think about what happens when Barry hasn't sold any paintings yet.
That means $x = 0$ .
Substituting $x = 0$ into our profit equation, $y = 6x - 1$ , we get $y = 6 \cdot 0 - 1$ .

This simplifies to $y = -1$ .
Remember, $y$ represents Barry's profit.
So, a profit of $-1$ means Barry has lost $\$1$ .
This loss represents the cost of the canvas because he hasn't made any money from selling paintings yet.

Therefore, the cost of the canvas was $\$1$ .

The cost of the canvas was $\$1$ .