Given: Two points of a line as shown below
[tex]\begin{gathered} Point1:(-2,-2) \\ Point2:(4,22) \end{gathered}[/tex]
To Determine: The equation of the line
Solution
The formula for finding equation of a line given two points is
[tex]\begin{gathered} Point1:(x_1,y_1) \\ Point2:(x_2,y_2) \\ \frac{y-y_1}{x-x_1}=\frac{y_2-y_1}{x_2-x_1} \end{gathered}[/tex]
Substitute the given points into the formula
[tex]\begin{gathered} \frac{y--2}{x--2}=\frac{22--2}{4--2} \\ \frac{y+2}{x+2}=\frac{22+2}{4+2} \\ \frac{y+2}{x+2}=\frac{24}{6} \\ \frac{y+2}{x+2}=4 \\ y+2=4(x+2) \\ y+2=4x+8 \\ y=4x+8-2 \\ y=4x+6 \end{gathered}[/tex]
Hence, the equation of the line is y = 4x + 6, OPTION A
