Question

Use the points (2, 14) and (10, 22) to write the equation of the line of best fit shown

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Answer 1

The equation of the line best fit is y = x + 12

Explanation:

The form of the linear equation is y = m x + b, where

• m is the slope of the line

• b is the y-intercept

The rule of the slope is m =
`(y2-y1)/(x2-x1)` , where

• (x1, y1) and (x2, y2) are two points on the line

∵ The line passes through points (2, 14) and (10, 22)

∴ x1 = 2 and y1 = 14

∴ x2 = 10 and y2 = 22

→ Substitute them in the rule of the slope above to find it

∵ m =
`(22-14)/(10-2)=(8)/(8)=1`

∴ m = 1

→ Substitute it in the form of the equation above

∴ y = (1)x + b

∴ y = x + b

→ To find b substitute x by 2 and y by 14 in the equation

∵ 14 = 2 + b

→ Subtract 2 from both sides

∴ 14 - 2 = 2 - 2 + b

∴ 12 = b

→ Substitute it in the equation

∴ y = x + 12

∴ The equation of the line best fit is y = x + 12