Question

which of the following points is collinear with (1, 3), and (3, 5)? (2, 2) (4, 6) (5, 5) (-1, 2)

Explanation:

Step1: Find the slope between \((1,3)\) and \((3,5)\)

The slope formula is \(m=\frac{y_2 - y_1}{x_2 - x_1}\).
For \((x_1,y_1)=(1,3)\) and \((x_2,y_2)=(3,5)\), \(m=\frac{5 - 3}{3 - 1}=\frac{2}{2}=1\).

Step2: Use the point - slope form \(y - y_1=m(x - x_1)\)

Using \(m = 1\) and \((x_1,y_1)=(1,3)\), the equation of the line is \(y-3=1\times(x - 1)\), which simplifies to \(y=x+2\).

Step3: Check each point

• For \((2,2)\): Substitute \(x = 2\) into \(y=x+2\), \(y=2 + 2=4

eq2\).

• For \((4,6)\): Substitute \(x = 4\) into \(y=x+2\), \(y=4+2=6\).
• For \((5,5)\): Substitute \(x = 5\) into \(y=x+2\), \(y=5+2=7

eq5\).

• For \((-1,2)\): Substitute \(x=-1\) into \(y=x+2\), \(y=-1 + 2=1

eq2\).

Answer:

\((4,6)\)