Find the equation of the straight line joining
a)(4, 4) and ( 2, 0)
b)(3, -1), (5, 4)
i also need to know how you went about solving this problem so i can understand.. many thanks
take the generic straight line:
y=mx + b.
Put in the first point: (4,4)
4=4m+b let this be the equation 1)
put in the second point in the generic
0=2m+b
Now you have two equations, and two unknowns (m,b). Solve them. In this case subtract the second equation from the first, which yields
4=2m or m=2
This makes b=-4 check that.
A slight variation of bobpursey's method for #2
slope = (4+1)/(5-3) = 5/2
let the equation be y = (5/2)x + b
sub in the point (5,4)
4 = 5/2(5) + b
8 = 25 + 2b
b = -17/2
so y = (5/2)x - 17/2
To find the equation of a straight line joining two points, you can use the slope-intercept form of a line: y = mx + b, where m is the slope and b is the y-intercept.
a) To find the equation of the line joining (4, 4) and (2, 0):
Step 1: Calculate the slope (m):
The slope of a line passing through two points (x1, y1) and (x2, y2) can be found using the formula:
m = (y2 - y1) / (x2 - x1)
Plugging in the values, we get:
m = (0 - 4) / (2 - 4) = -4 / -2 = 2
Step 2: Calculate the y-intercept (b):
To find the y-intercept (b), we can substitute the coordinates of one of the points (say, (2, 0)) into the equation.
0 = 2(2) + b [Using the slope-intercept form, substituting m = 2 and (x, y) = (2, 0)]
0 = 4 + b
Therefore, b = -4
Step 3: Write the equation using the slope and y-intercept:
Using the values of m and b that we found, the equation of the line is:
y = 2x - 4
b) To find the equation of the line joining (3, -1) and (5, 4):
Step 1: Calculate the slope (m):
m = (4 - -1) / (5 - 3) = 5/2
Step 2: Calculate the y-intercept (b):
Using point (3, -1):
-1 = (5/2)(3) + b
-1 = 15/2 + b
b = -1 - 15/2 = -17/2
Step 3: Write the equation using the slope and y-intercept:
The equation of the line is:
y = (5/2)x - 17/2
By following these steps, you can find the equation of a straight line joining two points.