For all those math people! I REALLY NEED HELP!!!?

Question

The coordinates of two points are given. State the equation of the straight line joining these two points and whether the line is horizontal or vertical.

a. {(1,2,),(3,2)}

b. {(2,1),(2,3)}

c. {(0,5),(0, -5)}

d. {(5,0),(-5,0)}

e. {(10,5),(5,5)}

Answer 1

The equation of a line is given as y = mx+c
where m is the gradient and c is the y-intercept.

Now when two sets of coordinates are given, (x1,y1) (x2,y2), the gradient of the line is given as

m = (y2 - y1) / (x2 - x1)

Therefore

a) (1,2) (3,2)
Equation: y = 2
Line is horizontal

b) (2,1) (2,3)
Equation: x = 2
Line is vertical

c) (0,5) (0,-5)
Equation: x = 0
Line is vertical

d) (5,0) (-5,0)
Equation: y = 0
Line is horizontal

e) (10,5) (5,5)
Equation: y = 5
Line is horizontal

Answer 2

y = mx + b
slope m = y2 -y1/ x1-x2
0/-2 = 0
Now I have the slope and two points. I know I can find the equation (by solving first for "b") if I have a point and the slope. So I need to pick one of the points (it doesn't matter which one), and use it to solve for b. Using the point (1, 2), I get:

Y = mx + b
2 = 0(1) + b
b = 2
so the equation is Y = (-0/2)x + 2 which is just Y = 2
using the same method
b) m = 2/0 which is not possible to solve
c) m = -10/0
d) m = 0/10 = 0 so Y = 0 + 0 = 0
e) m = 0/5 = so Y = 0 + 5 = 5

Answer 3

a y = 2 horizontal

b x = 2 vertical

c x = 0 vertical

d y = 0 horizontal

e y =5 horizontal

Answer 4

the equation for the straight line is

(y2-y1)=m(x2-x1)

and m=(y2-y1)\(x2-x1)...
first u need to find the slope (m) for individual lines and then
putting the points in the above equation u will get the equationof a line

important thing:
if the x-cordinate is 0 then that line is a horizontal like the points
{(0,5),(0, -5)} line is parallel to x -axis

on the other hand if y cordinate is 0 that is {(5,0),(-5,0)} then the line will be parallel to y axis

Answer 5

any line with the same y coordinate is a horizontal line
any line with the same x coordinate is a vertical line

The rest, you need to find the slope, which is the change in y divided by the change in x. Then use the point slope formula to get the equation for the line.

Answer 6

a) Horizontal
b) Vertical
c) Vertical
d) Horizontal
e) Horizontal

Answer 7

Use y=mx+c

c being y intercept
m being the gradient
same y co-ordinates =zero gradient
same x co-ordinates also = zero gradient
therefore m=0
so if you sub in x and y values you will find c
so equation will read y=c
then just right in c value
put the equation in form y=mx+c (standard form of equation)