Question

Write the equation containing the points (-2,4) and (1,10).

Answer 1

y=2x+8

Explanation:

Given the two points:

`\begin{gathered} (x_1,y_1)=(-2,4) \\ \mleft(x_2,y_2\mright)=\mleft(1,10\mright) \end{gathered}`

In order to find the equation of the line connecting them, we employ the use of the two-points formula given below:

`(y-y_1)/(x-x_1)=(y_2-y_1)/(x_2-x_1)`

Substitute the values:

`(y-4)/(x-(-2))=(10-4)/(1-(-2))`

Next, simplify:

`\begin{gathered} (y-4)/(x+2)=(6)/(3)=2 \\ \implies y-4=2(x+2) \\ \implies y=2(x+2)+4 \\ \implies y=2x+4+4 \\ \implies y=2x+8 \end{gathered}`

The equation containing the points (-2,4) and (1,10) is y=2x+8.