GUITAR Lydia wants to purchase guitar
lessons. She sees a sign that gives the prices
for 7 guitar lessons and 11 guitar lessons.
Write a linear equation to find the total
cost for a lessons.

The answer would be C=10d+12

Hope this helps

Have a great day/night

The total cost for the guitar lessons includes an initial cost fee which is

added to the unit cost.

Where the cost of 7 lessons is a and the cost of 11 lessons is b, we have

Where the cost for 7 lessons is $82, and the cost of 11 lessons is $122, we have;

Reasons:

The general equation for the total cost of lessons is;

Let a represent the cost of 7 guitar lessons, and let b represent the cost of

9 guitar lessons, given that the cost increases linearly with the number of

lessons, we have;

The cost increase per lesson = The slope of the linear function representing the total cost of a guitar lesson

Therefore;

[tex]\displaystyle Slope = \frac{b - a}{11 - 7} = \mathbf{\frac{b - a}{4}}[/tex]

Expressing the equation in the slope and intercept form, we have;

[tex]\displaystyle (y - a) = \frac{b - a}{4} \cdot (x - 7)[/tex]

[tex]\displaystyle y = \frac{b - a}{4} \cdot x - 7 \times\frac{b - a}{4} + a = \frac{b - a}{4} \cdot x+ \frac{11\cdot a - 7 \cdot b}{4}[/tex]

[tex]\displaystyle y = \frac{b - a}{4} \cdot x+ \frac{11\cdot a - 7 \cdot b}{4} = \mathbf{\frac{1}{4} \cdot ((b - a) \cdot x + 11 \cdot a - 7 \cdot b)}[/tex]

Where, in a similar question, a = $82, b = $122, we have;

[tex]\displaystyle y = \frac{1}{4} \cdot(122 - 82) \cdot x+ \frac{1}{4} \cdot (11\times 82 - 7 \times 122)= 10 \cdot x + 12[/tex]

y = 10·x + 12

The total cost of a lessons is; y = 10 × 1 + 12 = 22

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