KS3 maths worksheets › Year 9 › Linear graphs Year 9 · Key Stage 3 · free KS3 maths worksheet Linear graphs
13 original questions, 45 marks. Type your answers below for an instant mark and a score (algebra in any equivalent form, e.g. 2sqrt(3) or 2√3), or print the worksheet, mark it with the answers sheet, and use the solutions to see every step written out by hand.
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1 A straight line has equation y = 3x − 2
Write down the gradient of the line. Write down the coordinates of the point where the line crosses the y -axis. 2 marks Show answer a) 3b) (0, -2)
2 Here is a table of values for y = 3x − 1
Complete the table. On the grid, draw the graph of y = 3x − 1 for values of x from −1 to 3 −2 −1 1 2 3 4 −5 −4 −3 −2 −1 1 2 3 4 5 6 7 8 9 O x y
4 marks Show answer a) -4, 2, 5b) straight line from (-1, -4) to (3, 8)
3 A straight line passes through the points A (2, 5) and B (6, 17).
Work out the gradient of the line.
2 marks Show answer 3
4 The line segment AB is drawn on the grid. A is the point (1, 2) and B is the point (4, 6).
Work out the gradient of AB. Work out the length of AB. 0 1 2 3 4 5 6 0 1 2 3 4 5 6 7 x y A B
4 marks Show answer a) 4/3b) 5 units
5 P is the point (−2, 5) and Q is the point (6, −1). Find the coordinates of the midpoint of PQ. M (3, 4) is the midpoint of the line segment AB. A is the point (1, −2). Find the coordinates of B. 4 marks Show answer a) (2, 2)b) (5, 10)
6 Here are the equations of two straight lines.
Line P: y = 4x − 3y = 2x + 5
Which line is steeper? Give a reason. Which line crosses the y -axis at the higher point? Give a reason. The two lines cross at one point. Work out the coordinates of this point. 4 marks Show answer a) Line P, because its gradient 4 is greater than 2b) Line Q, because it crosses at (0, 5) and P crosses at (0, -3)c) (4, 13)
7 On the axes, sketch the graphs of
y = 2x − 4y = 6 − 2x Mark the coordinates of the points where each line crosses the axes.
−3 −2 −1 1 2 3 4 5 −6 −5 −4 −3 −2 −1 1 2 3 4 5 6 7 O x y
4 marks Show answer a) line through (0, -4) and (2, 0), sloping up b) line through (0, 6) and (3, 0), sloping down
8 A straight line has gradient -2 and passes through the point (3, 1).
Find the equation of the line.
3 marks Show answer y = -2x + 7
9 The straight line L has equation y = 5x - 3
Write down the gradient of L. Find the equation of the straight line that is parallel to L and passes through the point (2, 11). 4 marks Show answer a) 5b) y = 5x + 1
10 Find the equation of the straight line that is perpendicular to y = 2x - 3 and passes through the point (4, 1).
3 marks Show answer y = -x 2
Extension questions: beyond the core Year 9 objectives, for pupils who want a stretch.
11 Write each equation in the form y = mx + c . Then write down the gradient of the line.
3x + 2y = 12 4y − 8x = 20 4 marks Show answer a) y = -1.5x + 6, gradient -1.5b) y = 2x + 5, gradient 2
12 On the grid, draw the graph of 2x + 3y = 12 for values of x from 0 to 6
0 1 2 3 4 5 6 7 0 1 2 3 4 5 6 x y
3 marks Show answer straight line from (0, 4) to (6, 0)
13 The straight line L has equation 3x + 4y = 8
Find the equation of the straight line that is parallel to L and passes through the point (8, 1).
4 marks Show answer y = -3x 4
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Every question here is original and written by Robinson Tuition. It follows the Key Stage 3 programme of study; Year 9 sheets end with extension questions for top sets.
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