Write an equation fort he line through the point (-1,2) and parallel to the line with equation 3x-2y-5=0. Write the equation in the general form.
We know that parallel lines have the same slope. Therefore, the line we are drawing will have the same slope as the equation 3x - 2y - 5 = 0.
However, to find the slope the equation must be in the form of: y = mx + b, where m = slope and b = y intercept.
3x - 2y - 5 = 0
2y = 3x - 5
y = (3/2)x - (5/2)
So, the slope of the line is: m = 3/2
We now know two pieces of information about the line, the slope is 3/2 and it goes through the point (-1, 2). Use the equation for point slope to generate the equation of our line:
(y - y1) = m (x - x1),
where m = 3/2, x1 = -1, y1 = 2
(y - 2) = (3/2) (x - (-1))
y - 2 = (3/2)x + (3/2)
y = (3/2)x + (7/2)
Answer: y = (3/2)x + (7/2)