Find the equation of the line that passes through (2,3) and (-3,3).
The equation of the line is:
Let us use one of the point (2,3)
==> y-3= m(x-2)
==> y= m(x-2)=3
Now let us calculate the slope (m):
m= y2-y1/(x2-x1)= 3-3/ -3-2= 0/-5=0
Then the slope m= 0
==> y= 3
That means that we have a horizontal line parallel to x axis and passes through y=3
Coordinates : (2,3) , (-3,3) , (x,y)
(3-3)/(-3-2) = (y-3)/[x-(-3)]
0 = (y-3)/(x+3)
0 = y-3
y = 3
A line which passes through 2 given points, A(2,3) and B(-3,3), has the following equation:
(xB-xA)/(x-xA) = (yB-yA)/(y-yA)
(-3-2)/(x-2) = (3-3)/(y-3)
-5/(x-2) = 0/(y-3)
We'll cross multiply:
-5(y-3) = 0(x-2)
-5y+15 = 0
We'll isolate -5y to the left side. For this reason, we'll subtract 20 both sides:
-5y = -15
We'll divide by -5:
y = 3
The equation of the line is y=3.
The general equation of a line is:
y = mx + c
m = slope of the line, and
c is the y coordinate of line where it intercepts the x-axis.
The slope of a line passing through any line passing through 2 points (x1, y,1) and (x2, y2) is given by:
Slope = (y2 -y1)/(x2 - x1)
Slope of line passing through the given points = m = (3 - 3)/-3 -2) = 0/-5 = 0
Thus the line is parallel to x-axis, and the value of m in equation of the line is 0.
As the y-coordinates of both the given points are 3, it is clear that this line intercepts y-axis at point (0, 3).
Therefore the value of c in equation of line is 3.
Substituting these values of m and c in the standard equation of line we get equation of line as:
y = 0*x + 3 = y
Equation of line is:
y = 3
Let us suppose that a line y = mx +c passes through the points (2,3) and (-3,3). Now our work is to find m and c by the conditions that the points (2,3) and (3, -3) satisfy the equation y = mx+c, or mx+c = y.
Since (2,3) satisfy mx+c = y, put x=2 and y = 3.
m(2)+c = 3.
2m+c = 3..................(1)
Similarly, the other point (3,3) also should satisfy mx+c = y. So,
3m+c = 3..................(2)
Now we solve for m and n from equations (1) and (2):
Eq(3)- Eq(1) eliminates c.
(3m+c)-(2m+c) = 3-3
m = 0.
Substituting m =0 in (1), c = 3.
So y= mx+c now becomes, y = 0x+3 . Or y =3 is the equation that passes through (2,3) and (3,3)..