Question

. The following chart shows the number of concert tickets sold and the profit earned. Find the slope of the line through these points
Tickets Sold Profit (dollars)
50 100
100 250
150 400
200 550

Answer 1

Answer:

the slope of the line through these points is 3

Step-by-step explanation:

Given that:

#Tickets #Sold Profit (dollars)

50                   100

100                  250

150                  400

200                 550

Find the slope of the line through these points

As we know, the slope of a linear line can be calculated as following:

m = Δy / Δx , where:

• Δy = y2 - y1
• Δx = x2 -x1

In this situation,

• let the point (50 100) is (x1, y1),
• let the point (100, 250) is (x2, y2),

We have the slope:

m = (250 -100) / (100 -50) = 150 / 50 = 3

So the slope of the line through these points is 3

Answer 2

Answer:

$y=3x-50$

Step-by-step explanation:

You are given the table

$\begin{array}{cc}\text{Tickets Sold}&\text{Profit}\\ \\50&100\\100&250\\150&400\\200&550\end{array}$

The linear equation of the line passing through the points $(x_1,y_1)$ and $(x_2,y_2)$ is

$y-y_1=\dfrac{y_2-y_1}{x_2-x_1}(x-x_1)$

Choose two points, for example, $(50,100)$ and $(100,250)$ and use the equation above:

$y-100=\dfrac{250-100}{100-50}(x-50)\\ \\y-100=\dfrac{150}{50}(x-50)\\ \\y-100=3(x-50)\\ \\y-100=3x-150\\ \\y=3x-50$

Check two remaining points:

$(150,400): \ \ 3\cdot 150-50=450-50=400\\ \\(200,550):\ \ 3\cdot 200-50=600-50=550$