IB Mathematics Applications & Interpretation 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 $(2,-1)$.