7. Graphs

Question 1

Gradient

Answer 1

Gradient = (Difference in y coordinates) / (Difference in x-coordinates)

Question 2

Find midpoint of line PQ

P = (2, 1)
Q = (6, 4)

Answer 2

Coordinates = [((2+6)/2), ((1+4)/2)]

Coordinates = [(8/2), (5/2)]

Coordinates = [4, 2.5]

Question 3

Equation of a line

Answer 3

y = mx+c

m = gradient
c = y intercept

Question 4

Finding the equation of a line passing through (1, 3) and (3, 7)

Answer 4

Gradient (m)= ((7-3) / (3-1)) = (4 / 2) = 2

y = 2x + c

Substitute in y and x values for one coordinate

3 = 2 * 1 + c
3 = 2 + c
c = 1

y = 2x + 1

Question 5

Gradient of perpendicular lines (equation)

Answer 5

Eg.

Gradient of line A = 2
Gradient of line B = -1/2

Gradient A * Gradient B = 2 * -1/2 = -1

Gradients of perpendicular lines always equals -1

Question 6

Estimating the gradient of a curve

Answer 6

The gradient of a curve is constantly changing. However, it is possible to estimate the gradient of a curve AT A CERTAIN POINT by drawing a tangent and calculating the gradient of the tangent.

Question 7

Equation of a reciprocal line

Answer 7

y = c/x

Question 8

Equation of a exponential graph

Answer 8

y = k^x

Question 9

Equation of a cubic graph

Answer 9

y = x^3

Question 10

Finding the derivative

Answer 10

y = kx^n

–> then

dy/dx = knx^n-1

Question 11

y = 3x² - 5x + 3

Derivative

Answer 11

dy/dx = 6x - 5

Question 12

Maximum vs Minimum point?

Answer 12

If the second derivative is positive, the turning point is a minimum point.

If the second derivative is negative, the turning point is a maximum point.