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Data was collected on the amount of time that a random sample of 8 students spent studying for a test and the grades they earned on the test. A scatter plot and line of fit were created for the data.

scatter plot titled students' data, with the x-axis labeled study time in hours and the y-axis labeled grade percent. Points are plotted at 1 comma 65, 2 comma 60, 2 comma 70, 2 comma 80, 3 comma 70, 3 comma 90, 4 comma 85, and 4 comma 90, and a line of fit drawn passing through the points 0 comma 50 and 2 comma 70

Determine the equation of the line of fit.

y = 5x + 50
y = 5x + 70
y = 10x + 50
y = 10x + 70

Sagot :

chibabykalu16

Answer:

y = 10x + 50

Step-by-step explanation:

To determine the equation of the line of fit from the scatter plot data, we need to use the coordinates of two points that the line passes through. Given points are (0, 50) and (2, 70).

1. Find the slope (m):

The formula for the slope [tex] \sf m [/tex] is:

[tex] \sf m = \frac{y_2 - y_1}{x_2 - x_1} [/tex]

Using the points [tex] \sf (0, 50) [/tex] and [tex] \sf (2, 70) [/tex]:

[tex] \sf m = \frac{70 - 50}{2 - 0} = \frac{20}{2} = 10 [/tex]

2. Determine the y-intercept ([tex] \sf b [/tex]):

The equation of a line in slope-intercept form is:

[tex] \sf y = mx + b [/tex]

Using the point [tex] \sf (0, 50) [/tex]:

[tex] \sf 50 = 10 \cdot 0 + b \implies b = 50 [/tex]

3. Write the equation of the line:

Substitute the slope [tex] \sf m [/tex] and y-intercept [tex] \sf b [/tex] into the slope-intercept form:

[tex] \sf y = 10x + 50 [/tex]

Thus, the equation of the line of fit is:

  • y = 10x + 50
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