find the equation of the straight line passing through P -2,1and parallel to the line with equation 2x - 3y=1​

Step-by-step explanation:

Parallel lines have the same slope. Therefore, the line we're trying to find the equation for and the given line 2x-3y=1​ must have the same slope.

1) Find the slope of 2x-3y=1​

To do this, rewrite this equation in slope-intercept form: where is the slope and is the y-intercept (the value of y when the line crosses the y-axis)

Subtract 2x from both sides

Divide both sides by -3 to isolate y

Now, we can easily identify that is in the position of m, the slope. Plug this into :

2) Find the y-intercept

To find the y-intercept, plug the given point P(-2,1) into the equation and solve for b

Add to both sides of the equation

Therefore, the y-intercept of the line is . Plug this into our original equation:

I hope this helps!