Final answer:
To find the equation of a line that approximates the data using the ordered pairs (3,5.8) and (7.8,8), calculate the slope using the formula m = (Y2 - Y1) / (X2 - X1), then use one of the ordered pairs to find the y-intercept and write the equation in slope-intercept form y = mx + b.
Step-by-step explanation:
To find the equation of a line that approximates the data using the ordered pairs (3,5.8) and (7.8,8), we can calculate the slope using the formula:
m = (Y2 - Y1) / (X2 - X1)
Plugging in the values, we get:
m = (8 - 5.8) / (7.8 - 3)
m ≈ 0.4436
The slope-intercept form of a line is given by y = mx + b, where m is the slope and b is the y-intercept. To find the y-intercept, we can use one of the ordered pairs. Let's use (3,5.8):
5.8 = 0.4436(3) + b
Simplifying, we get:
b ≈ 4.57
Therefore, the equation of the line that approximates the data is:
y ≈ 0.4436x + 4.57