Question

A scatter plot of data compares the number of posters (x) sold and its price in dollars (y). It

contains the ordered pairs (20,12) and (30,15). Write an equation in slope intercept form for
the line of fit for this situation. Use this prediction equation to estimate how many dollars 50
posters would cost.

Answer 1

The equation in slope-intercept form for the line of fit is y = 0.3x + 6. Using this equation, 50 posters would cost approximately 21 dollars.

Step-by-step explanation:

To write an equation in slope-intercept form for the line of fit using the ordered pairs (20, 12) and (30, 15), we first calculate the slope (m) using the formula Δy/Δx, which is the change in y over the change in x. The slope calculation gives us:

(15 - 12) / (30 - 20) = 3 / 10 = 0.3

Now we have the slope, m = 0.3. To find the y-intercept (b), we can use one of the points. Plugging in the values of one ordered pair to the equation y = mx + b gives us:

12 = 0.3(20) + b
12 = 6 + b
b = 12 - 6
b = 6

Thus, the y-intercept is 6. The equation of the line in slope-intercept form is:

y = 0.3x + 6

To predict the cost for 50 posters, we use this equation:

y = 0.3(50) + 6
y = 15 + 6
y = 21

Hence, 50 posters would cost approximately 21 dollars.