Problem Set
Equation of a Line
1. Find the equation of the line which passes through the points (5,1) and has a slope of .5.
In this case the slope and one set of coordinates are known. This case involves the use of the point-slope formula.
The point-slope formula
y = y1 + b (x - x1)
y = 1 + .5(x-5)
y = 1 + .5x – 2.5
y = -1.5 + .5x
2. Find the equation of the line which passes through the points (2,0) and has a slope of 1.
In this case the slope and one set of coordinates are known. This case involves the use of the point-slope formula.
The point-slope formula
y = y1 + b (x - x1)
y = 0 + 1(x-2)
y = x - 2
y = -2 + x
3. Find the equation of the line which passes through the points (5, -2) and has a slope of -.5.
In this case the slope and one set of coordinates are known. This case involves the use of the point-slope formula.
The point-slope formula
y = y1 + b (x - x1)
y = -2 + -.5(x-5)
y = -2 - .5x + 2.5
y = .5 - .5x
4. Find the equation of the line which passes through the points ( 3, -2) and (1, 5).
In this case two sets of coordinates are known but the slope is not known. This case involves the use of the two-point formula. Since the slope of a linear function is the same at any point on the line we may set an expression for the value of the slope at one point equal to the value of the slope at any other point.
This expression is the two-point formula.
x1 = 3 y1 = -2
x2 = 1 y2 = 5
5. Find the equation of the line which passes through the points ( 1,0) and (0,1).
In this case two sets of coordinates are known but the slope is not known. This case involves the use of the two-point formula. Since the slope of a linear function is the same at any point on the line we may set an expression for the value of the slope at one point equal to the value of the slope at any other point.
This expression is the two-point formula.
x1 = 1 y1 = 0
x2 =
0
y2 =
1
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