Question

what is the equation of the line that is parallel to the given line and passes through the point (2, 3)?​

Answer 1

Given problems:

    Line parallel that passes through (2,3);

Solution:

To solve this problem, we need to first understand what parallel lines are.

A parallel line is any two line that does not meet at any point.

In order to achieve this, both lines must have the same slope.

 So, we find the slope of the given line and write in the form for a straight line.

 Slope of line  = $\frac{y_{2} - y_{1} }{x_{2} - x_{1} }$

      let   x₁, y₁ = (-2, -1)

              x₂, y₂ = (2 , -3)

Now input the parameters and solve for the slope;

            Slope of line = $\frac{-3-(-1)}{2- (-1)}$   = $\frac{-2}{3}$

Any line that would be parallel to this must have the same slope.

 Equation of a straight line;

                  y  = mx + c;

      y and x are the coordinates;

      m is the slope

      c is the y-axis intercept;

       From  (2, 3);

        y = 3 and x = 2; m = $\frac{-2}{3}$

     3 = $\frac{-2}{3}$ x 2 + C

     3 = $-\frac{4}{3}$ + C

       C = $\frac{13}{3}$

 So the equation of the line is;

               y = $\frac{-2}{3} x$  + $\frac{13}{3}$

 Multiply through by 3;

              3y = -2x + 13

The equation of the line is 3y = -2x + 13