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.
Algebra 2 Summer Review
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)
If the line is given in the form ax+by+c=0 then coefficients a and b give the direction perpendicular to the line. If you know vectors, those are the coordinates of a vector directed perpendicular to the line. Anyway, we know from geometry that a line perpendicular to one of the two parallel lines is perpendicular to another one too. So the line parallel to the given one 3x-2y-5=0 has to have the same coefficients a and b because the direction perpendicular to it is the same direction, which is perpendicular to the line 3x-2y-5=0. So it is in the forms 3x-2y+c=0. The c coefficient is found by plugging in the coordinates of a point, through which the line passes, that is (-1,2). The result is: 3*(-1)-2*2+c=0 or -7+c=0. It is easy to see now that c=7. The line equation is thus 3x-2y+7=0.
Aasiya -- for parallel lines "keep x & y the same" and "find the new number" ... 3x-2y = ? ... 3(-1) - 2(2) = -7 ==> 3x-2y = -7 ... Regards :)
General or standard form of linear equation is
Ax + By = C (A ≥ 0)
and final answer will be
3x – 2y = - 7