Question

To sketch the line of best fit, follow these steps:

Use the "Line" Button:

You need a straight line that best represents the trend of the data points. The "Line" button allows you to draw this.
The "Point" button is for marking individual points, which is unnecessary for drawing the line of best fit.
Choosing Two Points for the Equation:

Look for two points that seem to be along the general trend of the data.
Good choices appear to be:
(4, 30)
(12, 80)
These points are well-spaced and follow the overall upward trend.
Finding the Slope:
Use the slope formula:

m
=
y
2
−
y
1
x
2
−
x
1
m=
x
2
​
−x
1
​

y
2
​
−y
1
​

​

m
=
80
−
30
12
−
4
=
50
8
=
6.25
m=
12−4
80−30
​
=
8
50
​
=6.25
Equation of the Line:
Using
y
=
m
x
+
b
y=mx+b, plug in one of the points (e.g.,
(
4
,
30
)
(4,30)) to solve for
b
b:

30
=
6.25
(
4
)
+
b
30=6.25(4)+b
30
=
25
+
b
30=25+b
b
=
5
b=5
So, the equation of the line of best fit is:

y
=
6.25
x
+
5
y=6.25x+5
Solving for 75% Score:
Assuming a test score of 75, solve for
x
x:

75
=
6.25
x
+
5
75=6.25x+5
70
=
6.25
x
70=6.25x

Answer 1

To solve for \( x \) when the test score is 75, you start from the equation of the line of best fit you found, which is:

\[
y = 6.25x + 5
\]

You need to set \( y \) equal to 75:

\[
75 = 6.25x + 5
\]

Next, subtract 5 from both sides to isolate the term with \( x \):

\[
75 - 5 = 6.25x
\]

\[
70 = 6.25x
\]

Now, divide both sides by 6.25 to solve for \( x \):

\[
x = \frac{70}{6.25}
\]

Calculating \( x \):

\[
x = 11.2
\]

This means that a score of 75 corresponds to an \( x \) value of approximately 11.2 on your line of best fit.

Final summary:

- The equation of the line of best fit is \( y = 6.25x + 5 \).
- A test score of 75 corresponds to an \( x \) value of approximately **11.2**.