```Question 65150
A)write the point-slope equation form of the line which passes through the 2points: (6,0), (11,5)

We have two points on the and therefore we can easily calculate the slope:
m = (y2-y1)/(x2-x1) = 5/5 = 1
The point-slope eq. is:
y-y1 =m(x-x1) where x1, y1 can be any of the two points (6,0) or (11,5)
I'll let you substitute and do the final calculations

B) Write the point-slope equation form if the line which passes through the 2 points:(4, -8), (9, -5)

As we have done for point A, we need to first determine the slope:
m = (y2-y1)/(x2-x1) = 3/5
The point-slope form:
y-y1 = m(x-x1)
Now you only need to pick of the two points and substitute its coordinates for x1, y1 in the above equation

C) Write the general equation form of the line which passes through the 2 points: (6,0), (10, 5)

General form of an equation is:
Ax+By = C
One way to get to this form is to determine first the point-slope equation and then to convert it to the general form by placing x and y on one side and converting all coeficients to integers
So, let's first calculate the slope:
m = 5/4
Point-slope form is: y-0=5/4(x-6) or y = 5/4(x-6)
After bringing the equation to the form with the same denominator and then distributing we get to the general form: 5x-4y=6

D) Write the slope-y-intercept equation form of the line which passes through the 2 points: (-5, 1), (0, 4)

The slope-y-intercept equation form:
y = mx + b, where b is the y-intercept
Let first calculate the slope:
m=(3/5)
Now, to determine the y-intercept we can write the general form of the equation and then set x=0 and determine y.
Point slope form:
y-4 = (3/5)x
y = (3/5)x + 4
5y = 3x + 20
Set x = 0 and get y = 4. This is the y-intercept
Now let's write the slope-y-intercept form:
y = (3/5)x+4
Note: we could have arrived to the y-intercept (4) much easier if we have taken into consideration the (0,4) point given in text; this point basically gives us the y-coordinate when x = 0.

Hope it helped
Cristiana```