Question

Find the equation of the line passing through the points(4,2) and (6,10)

Answer 1

Step 1

Write the two points:

(4,2) and (6,10)

Step 2

Use the two points equation of a line formula to write the equation of a line.

`\begin{gathered} \left(4,2\right)and\text{ \lparen}6,10) \\ (x_1,\text{ y}_1)\text{ = \lparen4,2\rparen} \\ \\ (x_2,y_2)\text{ = \lparen6, 10\rparen} \\ (y-y_1)/(x-x_1)=(y_2-y_1)/(x_2-x_1) \end{gathered}`

Step 3

Substitute into the formula

`\begin{gathered} (y-2)/(x-4)=(10-2)/(6-4) \\ \\ (y-2)/(x-4)=(8)/(2) \\ \\ (y-2)/(x-4)=4 \\ \\ y\text{ - 2 = 4\lparen x-4\rparen} \\ \\ y\text{ - 2 = 4x - 16} \\ \\ y\text{ = 4x - 16 + 2} \\ \\ y\text{ = 4x - 14} \end{gathered}`

Final answer