Geometry, help?

Question

1. Write the equation of the line that passes through the points (-5, 1) and (-5,-2). Show all your work for credit.

2. Write the equation of a line in slope-intercept form that is parallel to the line 2x-5y= -8 and containing point (-5, 0). Show all your work for credit.

Answer 1

Q1: To find the slope; do (y1-y2)over (x1-x2)

so the slope would be:

-2-1 -3
------ = -----
-5+5 0

it is an undefined slope, and that makes it a vertical line, so it would be x= -5

Q2: since its parallel to 2x-5y= -8, then it will have the same slope; So you need to find the slope for that line:

-5y= -2x-8<------ minus 2x
y=2/5x+8/5<----- divided by 5

This tells us the slope is 2/5, so you just plug in the numbers to find out the y- intercept

0=2/5(-5)+b
0=-2+b
-2=b
so now we know the slope is 2/5 and the intercept is -2, just plug in the rest

y=2/5x-2

Answer 2

Problem #1
Let
(x1, y1) = (-5, 1)
(x2, y2) = (-5, -2)

What do your coordinates tell you? Did you notice that both x coordinates are the same? This line is vertical, so you would write the answer as x = -5

Here is how you solve a typical equation defined by two points:

The slope intercept equation is written as y = mx + b

Where m is the slope, b is the y-intercept.

Slope is defined as the change in elevation (change in y) divided by the change in horizonal movement (change in x)

Let
x1, y1 = -5, 1
x2, y2 = -5, -2

m = (y2-y1)/(x2-x1)
You notice that x2-x1 = 0, so your slope is mathematically considered undefined - or vertical, and from the two points given, x = -5.

If (y2-y1) = 0, then your line is horizontal.

Problem #2.
Take your equation and solve for y.

y = 2x/5 + 8/5.

Using y = mx +b, you now know that the slope is 2/5

So using the (-5, 0) and the slope, you get:

0 = (2/5) * -5 + b. Solve for b, and you find b = -2

So your equation becomes:
y = 2x/5 -2

Answer 3

1. y=-5
when computing the slope (y2-y1/x2-x1) you get m=0
2. solve for y==>y = 2/5x -8/5, put in point slope form using the points given==> y=2/5(x+5) -8/5

Answer 4

1)
m = (y2 − y1) ÷ (x2 − x1)
m = ((-2) − 1) ÷ (-5 − (-5))
m = -3 ÷ 0
UNDEFINED. The line is a vertical line.

2)
2x − 5y = (-8)
-5y = -2x − (-8)
y = (2/5)x − (8/5)

y = (2/5)x + b
0 = (2/5)(-5) + b
0 = -2 + b
b = 2
y = (2/5)x + 2