The cost for 5 dance lessons is $67. The cost for 7 lessons is $95. Write and solve an equation to find the cost of 13 lessons. Let x represent the number of lessons and y the cost of the lessons.

Equation(using the first sentence):

Cost:

To solve for the cost of 13 lessons, we first need to create an equation using the information provided.

We know the cost for $ x $ dance lessons corresponds to $ y $ dollars. The two points we can derive from the given data are:
- For 5 lessons: $ (x_1 = 5, y_1 = 67) $
- For 7 lessons: $ (x_2 = 7, y_2 = 95) $

### Step 1: Find the slope (rate per lesson)
The slope of the line between these two points is given by the formula:
\[
m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{95 - 67}{7 - 5} = \frac{28}{2} = 14
\]
So, the rate per lesson is $14 per lesson.

### Step 2: Use the point-slope form to write the equation
The point-slope form of a line is:
\[
y - y_1 = m(x - x_1)
\]
Using the point $ (5, 67) $ and the slope $ m = 14 $:
\[
y - 67 = 14(x - 5)
\]
Simplifying:
\[
y - 67 = 14x - 70
\]
\[
y = 14x - 3
\]

### Step 3: Find the cost for 13 lessons
Now, substitute $ x = 13 $ into the equation:
\[
y = 14(13) - 3 = 182 - 3 = 179
\]

Thus, the cost for 13 dance lessons is **$179**.

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Would you like further details or have any questions?

### Related Questions:
1. How can we derive a similar equation if the cost per lesson decreases?
2. How would you solve this if the pricing structure changed at a certain number of lessons?
3. Can you write the equation in slope-intercept form for any general lesson-cost problem?
4. What if the rate wasn't constant between lessons—how would the solution change?
5. How would you interpret the y-intercept of this equation in a real-life scenario?

### Tip:
To better understand linear equations, remember that the slope represents how quickly one variable changes with respect to the other—in this case, the cost per additional lesson.

The cost for 5 dance lessons is $67. The cost for 7 lessons is $95. Write and solve an equation to find the cost of 13 lessons. Let x represent the number of lessons and y the cost of the lessons.

Learn how to find the cost of 13 dance lessons by solving a linear equation. This problem involves calculating the slope between two points and using the point-slope and slope-intercept forms of a line. Suitable for students in Grades 7-10.

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