Module 3B Sketching Linear Graphs

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1 Year 10 Core Mathematics Module 3B Sketching Linear Graphs Name: Contents: Pre Test: Linear Graphs (MOL 4195) Set 1 Finding the Gradient (Graphing Method) Set 2 The Gradient Formula (Gradient of a line joining two points) (MOL 4191) Set 3 The equation of a Straight Line (MOL 8189) Set 4 Sketching Linear Graphs using Gradient and y-intercept Set 5 Sketching Linear Graphs using the x- and y- intercept (MOL 8151) Set 6 Finding the Linear equation given a Sketch Graph (4193) Set 7 Determining Linear Equations Set 8 Identifying Linear Inequations (MOL 4237) Set 9 Graphing Linear Inequations (MOL 4238) SAC Test Set (1-9) inclusive. Media Files: As per Maths OnLine Assessment: An in-class SAC covering set ( 1-9) inclusive.

2 Set 1 Finding the Gradient (Graphing method) Graph the points and find gradient using m _ rise run 1. Plot the points (0, 2) and (4, 3) and find gradient. 2. Plot the points (0, 3) and (2, 1) and find the gradient 3. Plot the points (0, 1) and (1, 4) and find the gradient 4. Plot the points (0, 3) and (4, 1) and find the gradient. 5. Plot the points (0, 1) and (1, 3) and find the gradient. 6. Plot the points (0, 3) and (3, 1) and find the gradient. 7. Plot the point (0, 2) and (1, 2) and find the gradient. 8. Plot the point (0, 4) and (2, 6) and find the gradient.

3 9. Plot the points (0, -2) and (1, 4). and find gradient. 10. Plot the points (-4, 6) and (5,3) and find the gradient. 11. Plot the points (2, -1) and (7, -1) and find the gradient. 12. Plot the points (-5, 3) and (-4, 9) and find the gradient. 13. Plot the points (6, 4) and (3, 2) and find the gradient. 14. Plot the points (03, 4) and (3, -4) and find the gradient. 15. Plot the point (-2, 3) and (2, 2) and find the gradient. 16. Plot the point (0, 2) and (-1, -1) and find the gradient Set 1 Answers: 1 m = 4 2) m = 2 3) m = 5 1 4) rn = ) m = 4 Finding Gradient (Graphing Method) 6) in = 2 3 7) = 4 8) in =1 9) m = ) 171 = ) m = 0 12) m = ) m = ) undefined 1 15) in = ) Ill = 3

4 Set 2 The Gradient Formula - Worksheet Use the Gradient Formula to find the gradient of the line joining each pair of points: Y2 - Yi m r. - '2 - IL Q1 A(3, 2) ; B(12, 4) Q6 F(-2, -2) ; G(3, -3) Q2 B(4, -3) ; C(-2, 0) Q7 Ii(-10, 5) ; 1(5, -8) Q3 MO, 4) ; N(8, 5) Q8 Y(0, 0) ; Q(3, 0) Q4 X(4, -3) ; Y(-4, 3) Q9 P(7, 3) ; D(4, -3) Q5 D(1, -5) ; E(-5, 1) Q10 1-1(15, 20) ; M(-5, 0) ANSWERS H) -5 D J) K) L) -4 M) 2 N) O) fl P) Ql -1 R) S) 6 T) 0 u)

5 Set 3 The Equation of a Straight Line - Worksheet QI ANSWERS A) y=5x-3 Q1 Write the equation of the straight line with the given gradient, m, and y-intercept, c: (i) m=2; c=6 (vi) m = c = 4 B) y= 2.3x+ C) y=5 D) y=2x+6 (ii) m = 5; c = 3 (iii) m = 8; c = 0 (iv) m = 3; c = 2 (v) m = 0; c=5 (vii) m = 2; c =1+ (viii) m = 4 c = 4 (ix) m = 0.2; c = 0.5 (x) m = 2.3; c = E) y F) y = ix +2.3 G) y = 3x +2 H)y=ix+4 I) y = x.1) y=li-2x y =8x Q2 Write down they-intercept, c, for each of these straight lines: (i) y = 2x 4 (ii) y = 5x + 2 (iii) y = 7 +3x (iv) 7y = 5 2x (v) 5y = 2x-30 (vi) 2x 3y = 9 (vii) 3x 5 = 0 2 Q2 ANSWERS 30 1) --} 10 J) 9 K) I 6 L) 4 M) 2 3 N) ) P) 7 Q3 Write down the gradient, in, for each of these straight lines (i) y = 3 3x (ii) y = (iii) 3x + 5y 8 = 0 (iv) 2y +3x = 0 (v) 5x 4y 12 = 0 (vi) 7x + 6y 18 = 0 2y (vii)--1 = 0 3 Q3 ANSWERS A) 5 H) B) 3 I) C) 4 j) 7 8 D) K) 3 E) 1 L) 2 F) M) G) 2

6 Set 4 Sketching Lines Using Gradient and Y-Intercept 1) Sketch the graph of each line by plotting its y-intercept and then using its slope a) y = 2x b) y = 5x 1 c) y = --x 2 d) y=4x+1 e) y = 3x 7 f) y = 2x + 3 g) y = 5x 4 h) y = 7 x i) y = 10 j) y = 3.4 k) y = 8x

7 Set 5 Graphing Straight Lines using X-Y Intercepts - Worksheet Sketch these lines using the x and y-intercepts. Clearly label each line with its equation. Q1 y=x+2 Q11 x+y+3 = 0 Q2 y =x-4 Q12 5 =x y Q3 y= 2x-5 Q13 5 =x+2y Q4 y=3 x Q14 y=t+1 Q5 y= Q15 Q6 x+y= 6 Q16 y = 3x Q7 x y=7 Q17 y=-2x Q8 y = 3-2x Q18 y = Q9 y = 3x 5 Q19 y-4x = 0 Q10 2x+y = 5 Q20 x+2y+6=0

8 Finding the Equation Given a Diagram - Worksheet Set 6 Write the equation of each line: Q 1 Q2 Q3 Q4 Q6 Q7 Q8 Q9 ANSWERS A) y=x B) y =4x+4 C) y ++1 D) y =10 fx E) y = 2 F) y=ix+2 G)y=x+2 H) ix-9 I) y =2x+2.1) y= x-1 K) y = x-1 L) y =1 ix M)y=x+1 N) y =1-3x 0) y=10-5x P) rix+4 Q) y = 4-4x R) y =ix+2 S) y=5x+10 y = x U) y = 2x V) y =1 x Q5 Q 1 W) y =ix X) y =3x-9 Y) y = 3x 9 Z) y9 }x

9 Set 7 Determining linear equations Determine the equation for each of the straight lines shown. a vi a Determine the equation of each of the straight lines shown. vi 4 W7P Find the linear equation given the information in each case below. a Gradient = 3, y-intercept = 3 b Gradient = -3, y-intercept = 4 c Gradient = -4, y-intercept = 2 0 d Gradient = 4, y-intercept = 2 e Gradient = -1, y-intercept = -4 * f Gradient = 0.5, y-intercept = -4 g Gradient = 5, y-intercept = 2.5 h Gradient = -6, y-intercept = 3 i Gradient = -2.5, y-intercept = 1.5 j Gradient = 3.5, y-intercept = E For each of the following, find the equation of the straight line with the given gradient and passing through the given point. a Gradient = 5, point = (5,6) b Gradient = -5, point = (5,6) c Gradient =- -4, point = (-2, 7) d Gradient = 4, point = (8, -2) e Gradient = 3, point = (10, -5) f Gradient = -3, point = (3, -3) g Gradient = -2, point = (20, -10) h Gradient = 2, point = (2, -0.5) i Gradient = 0.5, point = (6, -16) j Gradient = -0.5, point = (5, 3)

10 Set 7 Answers Determining linear equations 1 a y=2x+ 4 b y=-3x+12 c 5 d v= 2x 8 e f g y= 7x 5 h y=-3x 15 - i 2 a y=2x b y=-3x C y=x d y=3x+3 C y=-4x+ 2 e yrn x-4 g y= 5x+ 2.5 y=-2,5x a y=5x 19 C y=-4x 1 e y= 3x 35 g y= i 0.5x 19 b y=-33:+4 d y=4.x+ 2 y=0.5x 4 h y=-6x+3 j y = 3.5x b y=-5x+ 31 d y=tvf y=-3x+6 h y= 2x 4.5 j y =-0,5x+ 5.5

11 Set 8 Identifying Linear Inequalities - Worksheet Q1 Test a point from one side of each line then shade the region described by the inequation. (i) x-3 4 Y (ii) y 4 x 4Y (in) (vi) ; (ix) y x NOTE: You will have to test a point that is NOT on the line! / Q2 Writc an inequality for each of these regions. ie. in (i), is the inequality y.3x+2 or y.3x+2? (in (i) y=3x+2 = 5

12 Set 9 Graphing Linear Inequalities - Worksheet Draw a sketch of the region given by each inequality: Q1 y?_x+2 Q6 y_x+2 Q2 yx-3 Q7 3x y>6 Q3 y2x+4 Q11 x+2y<1 Q4 Q9 yflx+4 Q13 x+y_?1 Q10 x+y+1<0 ) Y 1,?c?kik k"td* NIX$NkWki4 4 \ nhkkt,\ \ SA\ 00Wik H trjk, I WAs WiNka k -1 I;

Math M111: Lecture Notes For Chapter 3

Section 3.1: Math M111: Lecture Notes For Chapter 3 Note: Make sure you already printed the graphing papers Plotting Points, Quadrant s signs, x-intercepts and y-intercepts Example 1: Plot the following