Question

11.) Write the equation of the line that passes through the given point P and its PARALLEL to the line with the givenequation. P(-1,2), y = 2/3x - 2

Answer 1

`y=(2)/(3)x+(8)/(3)`

Step-by-step explanation

When a line is parallel to another line, they have equal slopes.

This means that the slope of the line is:

`m=(2)/(3)`

To find the equation of the line, apply the point-slope method:

`y-y_1=m(x-x_1)`

where (x1, y1) is the point the line passes through.

Therefore, we have:

`\begin{gathered} y-2=(2)/(3)(x-(-1)) \\ y-2=(2)/(3)(x+1) \\ y-2=(2)/(3)x+(2)/(3) \\ y=(2)/(3)x+(2)/(3)+2 \\ y=(2)/(3)x+(8)/(3) \end{gathered}`

That is the equation of the line.