Straight line Graphs, Gradient of a curve and drawing tangents to a Curve

CONTENT

• Gradient of a Straight Line.
• Gradient of a Curve.
• Drawing of Tangents to a Curve.

Plotting a Straight line graph

Gradient of a Straight Line.

Gradient of a Curve. Drawing of Tangents to a Curve.

GENERAL EVALUATION/ REVISION QUESTIONS

1. A straight line passes through the points (3,k) and (-3,2k). If the gradient of the line is -2/3, find the value of k. What is the equation line?

2. Sketch the following graphs using gradient-intercept method.

a) y= 0.5x – 3      b) y= 5x       c)  y = x/4   –  3      d)   2y-10  = 2x

3. Find the gradients of the curves at the points indicated.

a) y= 6x –  x²   at  x= 3       b)   x² – 6x + 5

WEEKEND ASSIGNMENT

1. Find the gradient of the equation of line 2y – 10 = 2x   A. 1   B.  2    C.  3   D.    4

2. Find the gradient of the line joining (7,-2) and (-1,2)    A. ½   B. – ½   C.  1/3  D. -1/3

3. Find the equation of a straight line passing through (-3,-5) with gradient 2.

A. y =3x-1  B. y=2x-1C. y=2x-1   D. y=3x+1

Given that 3y-6x +15=0, use the information to answer questions 4 and 5.

4. Find the gradient of the line.     A. 5  B.  -5     C.   2    D.  -2

5. Find the intercept of the line. A. 5  B.  -5     C.   2    D.  -2

THEORY

1. Draw the graph of y= 2x-3 using convenient points and scale. Hence , find the gradient of the line at any convenient point.

2a) Copy and complete the following table of values for the relation y= 2x² – 7x-3.

X	-2	1-	0	1	2	3	4	5
Y	19		-3		-9

b) Using 2cm to 1unit on the x-axis and 2cm to 5units on the y-axis, draw the graph of y= 2x² -7x-3 for -2x≤5.

c) From your graph, find the:

i. minimum value of y.

ii. the equation of the line of symmetry.

iii. the gradient of the curve at x=1.

Reading Assignment

New General Mathematics for SSS2, pages 190-192, exercise 16d.