Question

What is the equation for a line that passes through the points (-2,-2) and (4,22)?

Answer 1

Given: Two points of a line as shown below

`\begin{gathered} Point1:(-2,-2) \\ Point2:(4,22) \end{gathered}`

To Determine: The equation of the line

Solution

The formula for finding equation of a line given two points is

`\begin{gathered} Point1:(x_1,y_1) \\ Point2:(x_2,y_2) \\ (y-y_1)/(x-x_1)=(y_2-y_1)/(x_2-x_1) \end{gathered}`

Substitute the given points into the formula

`\begin{gathered} (y--2)/(x--2)=(22--2)/(4--2) \\ (y+2)/(x+2)=(22+2)/(4+2) \\ (y+2)/(x+2)=(24)/(6) \\ (y+2)/(x+2)=4 \\ y+2=4(x+2) \\ y+2=4x+8 \\ y=4x+8-2 \\ y=4x+6 \end{gathered}`

Hence, the equation of the line is y = 4x + 6, OPTION A