Question Type 2: Calculating the linear relationship between the data in the form y=ax+b Exercises

Find the equation of the line passing through $(0,0)$ and $(5,10)$, giving your answer in the form $y = mx + c$.

Using the method of least squares, determine the regression line $y = ax + b$ for the following data: $(-1, 0), (0, 1), (1, 1.8), (2, 2.3), (3, 3)$.

Show that the points $(0, 3)$, $(3, 9)$, and $(6, 15)$ lie on a line and determine its equation in the form $y = ax + b$.

Find the linear relation $y = ax + b$ that fits the points $(-1, -2)$, $(0, 1)$, and $(1, 4)$ exactly.

Write the equation of the line $y = ax + b$ passing through $(-1, 2)$ and $(3, 14)$. [3 marks]

Determine the equation of the line passing through the points $(2, 4)$, $(4, 10)$, and $(6, 16)$. Express your answer in the form $y = ax + b$.

Find, using the method of least squares, the equation of the line of best fit $y = ax + b$ for the data points $(1,2)$, $(2,5)$, $(3,7)$, and $(4,10)$.

Find the least-squares regression line $y = ax + b$ for the data $(1, 2), (2, 3), (3, 5), (4, 4)$.

Given the points $(1, 2)$, $(2, 5)$, and $(3, 8)$, show that they lie on a line $y = ax + b$ and find its equation.

Determine the regression line $y = ax + b$ for the data points $(0, 1), (1, 2), (2, 1.5), (3, 3.5)$ by the method of least squares.

Find the equation of the line $y = ax + b$ passing through the points $(1, 3)$ and $(4, 11)$.

Determine the equation of the straight line $y=ax+b$ passing through the points $(-2, 5)$ and $(2, -1)$.