For numbers (2) and (3), you need the concept of slopes. Generally, the slope of parallel lines are equal, while the slope of perpendicular lines are negative reciprocals of each other. An easy way to check for parallel and perpendicular lines is to make the equation of the line in the form y=mx+b. The m, or the coefficient of x, is the slope of the line. The b is called the y-intercept.

(2)

6x+2y = 4

2y = -6x + 4

y =-3x + 2

Since the slope is -3, the slope of the perpendicular line must be 1/3. So the equation of the line is:

y= 1/3 x + b

Since (-5,2) is a point of the line, we get the value of b by plugging in -5 for x and 2 for y.

2 = 1/3 (-5) + b

2 = -5/3 + b

2 + 5/3 = b

6/3 + 5/3 = b

11/3 = b

Therefore, the equation of the line is:

y = 1/3x + 11/3

This can also be written as:

3y = x + 11

or

x – 3y + 11 = 0

(3)

The slope of a line can also be obtained by using “rise over run”, or by getting the difference of the y’s over the difference of the x’s using any two points of the line. The formula looks like:

(Y2 – Y1) / (X2 – X1) given the points (X1, Y1) and (X2, Y2)

So the slope is

= ( 4 – 1) / ( 2 – (-2) )

= 3 / 4

Again, we use the format above and get the equation of the line to be:

y = 3/4 x + b

Again, we plug in values from the given point (1,5)

5 = 3/4 (1) + b

5 = 3/4 +b

5 – 3/4 = b

20/4 – 3/4 = b

17/4 = b

So, the equation of the line is:

y = 3/4 x + 17/4

or

4y = 3x + 17

or

3x – 4y + 17 = 0

Hope this helps.

-6(4/5)+5y=4

-4.8+5y=4

5y=8.8

y=1.76