Gradient and Intercept

1
Gradient and Intercept

• Geometry

2
Copy and complete the tables on the next slides.
Reminder The equation of a straight line
is given by y mx c where m gradient and
the line cuts the y axis at (0,c)
3
Equation of the line Gradient m Point where the line cuts the y axis
y 2x 7 2 (0,7)
y x - 5 1 (0,-5)
y 3x
y 4x - 1
y -3x -6
y -x -4
y 5x 8
y 2.5x 1
y -2x -3
Table 1
4
Equation of the line Gradient m Point where the line cuts the y axis
y 2x 7 2 (0,7)
y x - 5 1 (0,-5)
y 3x 3 (0,0)
y 4x - 1 4 (0,-1)
y -3x -6 -3 (0,-6)
y -x -4 -1 (0,-4)
y 5x 8 5 (0,8)
y 2.5x 1 2.5 (0,1)
y -2x -3 -2 (0,-3)
Table 1 - solutions
5
Equation of the line Gradient m Point where the line cuts the y axis
y 3x - 5
y 3.5x
y 2 4x
y -2 2x
y 1.5x
y 2.5x 4
y -2x
y 4 x
y -2.2x 8.9
Table 2
6
Equation of the line Gradient m Point where the line cuts the y axis
y 3x - 5 3 (0,-5)
y 3.5x 3.5 (0,0)
y 2 4x -4 (0,2)
y -2 2x -2 (0,-2)
y 1.5x 1.5 (0,0)
y 2.5x 4 2.5 (0,4)
y -2x -2 (0,0)
y 4 x 1 (0,4)
y -2.2x 8.9 -2.2 (0,-8.9)
Table 2 - solutions
7
Equation of the line Gradient m Point where the line cuts the y axis
2y 3x
x y 5 0
2x 3y 6 0
2x y 8
y 3x 7 0
2y x 1 0
4y x 1
2y 4 3x
y x 2 0
Table 3
8
Equation of the line Gradient m Point where the line cuts the y axis
2y 3x 3/2 (0,0)
x y 5 0 -1 (0,5)
2x 3y 6 0 -2/3 (0,2)
2x y 8 -2 (0,8)
y 3x 7 0 3 (0,7)
2y x 1 0 -1/2 (0,0.5)
4y x 1 ¼ (0,0.25)
2y 4 3x -3/2 (0,2)
y x 2 0 1 (0,2)
Table 3 - solutions
9
Equation of the line Gradient m Point where the line cuts the y axis
3y- x 6 0
2y x 2
4y 4 8x
2y x 1 0
3x 4y 12
8y 5x
x 4y 10 0
y 5
x 2y 0
Table 4
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Equation of the line Gradient m Point where the line cuts the y axis
3y - x 6 0 1/3 (0,2)
2y x 2 ½ (0,1)
4y 4 8x -2 (0,1)
2y x 1 0 ½ (0,0.5)
3x 4y 12 -3/4 (0,3)
8y 5x 5/8 (0,0)
x 4y 10 0 -1/4 (0,-2.5)
y 5 0 (0,5)
x 2y 0 1/2 (0,0)
Table 4 - solutions
11
Equation of the line Gradient m Point where the line cuts the y axis
y 2x 5 0
y 4 3x
x y 1 0
5y x 2
2x 3y 6 0
x 2y 4 0
3y 2x 1
10x y 7
2x y 0
Table 5
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Equation of the line Gradient m Point where the line cuts the y axis
y 2x 5 0 2 (0,5)
y 4 3x -3 (0,4)
x y 1 0 -1 (0,-1)
5y x 2 0.2 (0,0.4)
2x 3y 6 0 -2/3 (0,2)
x 2y 4 0 -1/2 (0,2)
3y 2x 1 2/3 (0,1/3)
10x y 7 -10 (0,7)
2x y 0 -2 (0,0)
Table 5 - solutions
13
Equation of the line Gradient m Point where the line cuts the y axis
y 4
4x 5y 20 0
2y x 8
y 3 - x
4x 2y 1 0
x 3y 12 0
2x 5y 10 0
4x y
x 5
Table 6
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Equation of the line Gradient m Point where the line cuts the y axis
y 4 0 (0,4)
4x 5y 20 0 -4/5 (0,4)
2y x 8 ½ (0,4)
y 3 - x -1 (0,3)
4x 2y 1 0 -2 (0,0.5)
x 3y 12 0 -1/3 (0,-4)
2x 5y 10 0 -0.4 (0,2)
4x y 4 (0,0)
x 5 undefined does not cut y axis
Table 6 - solutions