Page 170 - Mathematics

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11. Determine the equation of a straight line whose gradient is and passes
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through the point of intersection of two lines 3x − 2y = 2 and 2x − 3y = 3.
12. (a) Find the equation of a straight line whose gradient is 2 and passes
through the point (3,5).
(b) Determine the values of m and c such that the straight line y = mx c+

will pass through the points ( 1, 4)− and (3, 5).
(c) Find the value of y if the points A (3, y), B (0, 4), and C( 2, 8)− are
in the same line.
(d) Find the value of x so that the straight line joining the points A( , 5)x −
Tanzania Institute of Education
and B(2, 1) has the same slope as the line joining the points C(1, 5)
and D( 2, 1).− −
13. Find the equation for each of the following lines.
(a) Passing through the points (3, 3) and (1, 4) in the form ax by+ = . c
(b) Passing through the point(3, 4)− with gradient which is a negative
of the reciprocal of the gradient of the line 5x − 2y = 3.
14. Kiwengu is travelling by his car from Tanga. Before he starts the journey,
he makes sure that the fuel tank is full. After travelling a distance
of 50km, the odometer reaches 35 litres and when he travels further
150 km, the odometer read 25 litres. If x is the distance travelled and y
is the odometer reading;
(a) Draw a line on the xy-plane to represent the given information
(b) Determine the x and y-intercepts and give the meaning of these
information.
(c) Write the equation of the line drawn in (a)
(d) What is the slope of the line and what does it signify?
15. A family want to buy 8 loaves of bread. White bread costs Tshs 3,000
per loaf and brown bread costs Tshs 3,500 per loaf. The family can spend
Tshs 25,000 for that shopping. Find the number of each type of bread
the family can buy.
16. Juma is thinking of two numbers. Two times the first number is 3. Three
Mathematics Form One 17. A cafe sales tea and cakes. The first customer bought a cup of tea and two
times the first number is equal to the second number plus six. Find the two
numbers graphically by using any mathematical software of your choice.

cakes for Tshs 800. The second customer bought a cup of tea and a cupcake
for Tshs 500. Use any mathematical software of your choice to determine
graphically or algebraically the price of a cup of tea and a cake.

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Mathematics form 1.indd 164