Algebra 2 Summer Review

Question

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.

Answer 1

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)

Answer 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.

Answer 3

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 :)

Answer 4

General or standard form of linear equation is 
Ax + By = C (A ≥ 0)
~~~~~~~~

.......

and final answer will be
3x – 2y = - 7