Homework

Cartesian Coordinates and Graphs of Linear Equations

1. (a) State the coordinates of the points marked on the Cartesian plane below.

(b) On the same Cartesian plane, plot the following points.(i) F(0, –2) (ii) G(6, 5)(iii) H(–5, 0) (iv) I(4, –1)(v) J(–6, 3)

2. Answer the whole of this question on a sheet of graph paper.

(a) The table below shows the corresponding values of x and y for the equation y = x + 1.

x –2 0 2y a b c

(i) Find the value of a, of b and of c.(ii) Using a scale of 1 cm to represent 1 unit on both axes, draw the graph of

y = x + 1 for –2 ≤ x ≤ 2.

(b) The table below shows the corresponding values of x and y for the equation y = 3 – x.

x –2 0 2y d e f

(i) Find the value of d, of e and of f.(ii) Using a scale of 1 cm to represent 1 unit on both axes, draw the graph of

y = 3 – x for –2 ≤ x ≤ 2.

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3. Answer the whole of this question on a sheet of graph paper.

(a) The table below shows the corresponding values of x and y for the equation y = –4x.

x –2 0 1y a b c

(i) Find the value of a, of b and of c.(ii) Using a scale of 2 cm to represent 1 unit on the x-axis and 1 cm to represent 2

units on the y-axis, draw the graph of y = –4x for –2 ≤ x ≤ 1.

(b) The table below shows the corresponding values of x and y for the equationy = 3x + 2.

x –2 0 1y d e f

(i) Find the value of d, of e and of f.(ii) Using a scale of 2 cm to represent 1 unit on the x-axis and 1 cm to represent 2

units on the y-axis, draw the graph of y = 3x + 2 for –2 ≤ x ≤ 1.

4. Answer the whole of this question on a sheet of graph paper.

(a) The table below shows the corresponding values of x and y for the equationy = 2 – 2x.

x –1 0 2y g h i

(i) Find the value of g, of h and of i.(ii) Using a scale of 2 cm to represent 1 unit on the x-axis and 1 cm to represent 2

units on the y-axis, draw the graph of y = 2 – 2x for –1 ≤ x ≤ 2.

(b) The table below shows the corresponding values of x and y for the equationy = 3x – 5.

x –1 0 2y j k l

(i) Find the value of j, of k and of l.(ii) Using a scale of 2 cm to represent 1 unit on the x-axis and 1 cm to represent 2

units on the y-axis, draw the graph of y = 3x – 5 for –1 ≤ x ≤ 2.

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5. Answer the whole of this question on a sheet of graph paper.

The table below shows the corresponding values of x and y for the equation y = 2x + 6.

x –4 –2 0y a b c

(a) Find the value of a, of b and of c.(b) Using a scale of 2 cm to represent 1 unit on both axes, draw the graph of y = 2x + 6

for –4 ≤ x ≤ 0.(c) From the graph, find

(i) the value of y when x = –3.5,(ii) the value of x when y = 3.

6. Answer the whole of this question on a sheet of graph paper.

The table below shows the corresponding values of x and y for the equation y = –3x – 3.

x –2 0 1y d e f

(a) Find the value of d, of e and of f.(b) Using a scale of 2 cm to represent 1 unit on both axes, draw the graph of y = –3x – 3

for –2 ≤ x ≤ 1.(c) From the graph, find

(i) the value of y when x = –1.5,(ii) the value of x when y = –5.

7. Answer the whole of this question on a sheet of graph paper.

The table below shows the corresponding values of x and y for the equation 2y – 7x = 8.

x –6 –2 0y g h i

(a) Find the value of g, of h and of i.(b) Using a scale of 1 cm to represent 1 unit on both axes, draw the graph of 2y – 7x = 8

for –6 ≤ x ≤ 0.(c) From the graph, find

(i) the value of y when x = –2.6,(ii) the value of x when y = 0.5.

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8. Answer the whole of this question on a sheet of graph paper.

The table below shows the corresponding values of x and y for the equation 4y – x = –6.

x –6 –2 2y j k l

(a) Find the value of j, of k and of l.(b) Using a scale of 1 cm to represent 1 unit on the x-axis and 2 cm to represent 1 unit on

the y-axis, draw the graph of 4y – x = –6 for –6 ≤ x ≤ 2.(c) From the graph, find

(i) the value of y when x = –5.2,(ii) the value of x when y = –1.8.

9. Draw the following lines on the Cartesian plane below.

(a) x = 2 (b) y = 4.5(b) x = –5 (d) y = –3½(e) y = 1.8 (f) x = –0.6

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10. State whether each of the following straight lines is horizontal or vertical and the equation for each of the following straight lines.

11. Find the gradient of each of the following lines.(a)

(b)

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(c)

12. Answer the whole of this question on a sheet of graph paper.

The amount of savings, $S, that Jessica saves over a period of 16 weeks is given by the equation

S = 80 + 50w

where w represents the number of weeks passed.

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The table below shows the corresponding values of w and S for the equationS = 80 + 50w.

w 0 2 4 6 8 10 12 14 16S a b c d e f g h i

(a) Find the value of a, of b, of c, of d, of e, of f, of g, of h and of i.(b) Using a scale of 1 cm to represent 2 weeks on the w-axis and 1 cm to represent $100

on the S-axis, draw the graph of S = 80 + 50w for 0 ≤ w ≤ 16.(c) From the graph, find

(i) the amount of savings at the beginning of the 16-week period,(ii) the number of weeks she requires in order to save $800,(iii) the amount of savings after 11 weeks.

13. Answer the whole of this question on a sheet of graph paper.

The rental fee, R, in dollars, of a yacht is given by the equation

R = 5000 + 450t

where t is the duration in hours.

The table below shows the corresponding values of t and R for the equationR = 5000 + 450t.

t 0 1 2 3 4 5 6 7 8R a b c d e f g h i

(a) Find the value of a, of b, of c, of d, of e, of f, of g, of h and of i.(b) Using a scale of 1 cm to represent 1 hour on the t-axis and 1 cm to represent $1000 on

the R-axis, draw the graph of R = 5000 + 450t for 0 ≤ t ≤ 8.(c) From the graph, find

(i) the rental fee for renting a yacht for 4.5 hours,(ii) the number of hours that the yacht was rented if the rental fee was $8300.

End of Homework

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