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PLEASE HELP ASAP. WILL GIVE BRAINLIEST+30 POINTS!!!

Max makes and sells custom postcards. A graph of the line that represents Max's profit in dollars for the number of postcards sold passes through
(4,2) and (10,20).
What is Max's profit prior to selling any postcards? Enter the answer in the box.

Sagot :

semsee45

Answer:

-10

Step-by-step explanation:

Let x = number of postcards sold (as this is the independent variable)

Let y = profit (as this is the dependent variable)

We need to find the equation of the straight line that passes through the two points.

Find the gradient using the formula: [tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

where [tex]m[/tex] is the slope and [tex](x_1, y_1)[/tex]  and [tex](x_2, y_2)[/tex] are the two points

Let [tex](x_1, y_1)[/tex] = (4, 2)  and [tex](x_2, y_2)[/tex]  = (10, 20)

Therefore, [tex]m=\frac{20-2}{10-4}=\frac{18}{6} =3[/tex]

Now use the equation of line formula:  [tex]y-y_1=m(x-x_1)[/tex]

y - 2 = 3(x - 4)

y - 2 = 3x - 12

     y = 3x - 10

If Max doesn't sell any postcards, then x = 0.

Substituting x = 0 into the equation of the line:  y = (3 x 0) - 10 = -10

Therefore, Max's profit prior to selling any postcards is -10 (so he is at a net loss of 10 before selling any postcards).

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