? Drawing Straight Line Graphs | KS3 Maths | Beyond - Free Printable

I can see this is a worksheet about drawing straight-line graphs. Let me work through the problems shown on the right side of the worksheet (labeled "Your Turn").

Let me solve each problem step by step:

Problem 1: Draw the graph of y = x + 2 for values of x from -3 to 3

First, I'll create a table of values:
- When x = -3: y = -3 + 2 = -1 → Point: (-3, -1)
- When x = -2: y = -2 + 2 = 0 → Point: (-2, 0)
- When x = -1: y = -1 + 2 = 1 → Point: (-1, 1)
- When x = 0: y = 0 + 2 = 2 → Point: (0, 2)
- When x = 1: y = 1 + 2 = 3 → Point: (1, 3)
- When x = 2: y = 2 + 2 = 4 → Point: (2, 4)
- When x = 3: y = 3 + 2 = 5 → Point: (3, 5)

To draw: Plot these points and connect them with a straight line.

Problem 2: Draw the graph of y = 2x - 1 for values of x from -3 to 3

Table of values:
- When x = -3: y = 2(-3) - 1 = -6 - 1 = -7 → Point: (-3, -7)
- When x = -2: y = 2(-2) - 1 = -4 - 1 = -5 → Point: (-2, -5)
- When x = -1: y = 2(-1) - 1 = -2 - 1 = -3 → Point: (-1, -3)
- When x = 0: y = 2(0) - 1 = 0 - 1 = -1 → Point: (0, -1)
- When x = 1: y = 2(1) - 1 = 2 - 1 = 1 → Point: (1, 1)
- When x = 2: y = 2(2) - 1 = 4 - 1 = 3 → Point: (2, 3)
- When x = 3: y = 2(3) - 1 = 6 - 1 = 5 → Point: (3, 5)

To draw: Plot these points and connect them with a straight line.

Problem 3: Draw the graph of y = x - 4 for values of x from -3 to 3

Table of values:
- When x = -3: y = -3 - 4 = -7 → Point: (-3, -7)
- When x = -2: y = -2 - 4 = -6 → Point: (-2, -6)
- When x = -1: y = -1 - 4 = -5 → Point: (-1, -5)
- When x = 0: y = 0 - 4 = -4 → Point: (0, -4)
- When x = 1: y = 1 - 4 = -3 → Point: (1, -3)
- When x = 2: y = 2 - 4 = -2 → Point: (2, -2)
- When x = 3: y = 3 - 4 = -1 → Point: (3, -1)

To draw: Plot these points and connect them with a straight line.

Problem 4: Draw the graph of y = 3x + 1 for values of x from -3 to 3

Table of values:
- When x = -3: y = 3(-3) + 1 = -9 + 1 = -8 → Point: (-3, -8)
- When x = -2: y = 3(-2) + 1 = -6 + 1 = -5 → Point: (-2, -5)
- When x = -1: y = 3(-1) + 1 = -3 + 1 = -2 → Point: (-1, -2)
- When x = 0: y = 3(0) + 1 = 0 + 1 = 1 → Point: (0, 1)
- When x = 1: y = 3(1) + 1 = 3 + 1 = 4 → Point: (1, 4)
- When x = 2: y = 3(2) + 1 = 6 + 1 = 7 → Point: (2, 7)
- When x = 3: y = 3(3) + 1 = 9 + 1 = 10 → Point: (3, 10)

To draw: Plot these points and connect them with a straight line.

Problem 5: Draw the graph of y = ½x + 2 for values of x from -4 to 4

Table of values:
- When x = -4: y = ½(-4) + 2 = -2 + 2 = 0 → Point: (-4, 0)
- When x = -3: y = ½(-3) + 2 = -1.5 + 2 = 0.5 → Point: (-3, 0.5)
- When x = -2: y = ½(-2) + 2 = -1 + 2 = 1 → Point: (-2, 1)
- When x = -1: y = ½(-1) + 2 = -0.5 + 2 = 1.5 → Point: (-1, 1.5)
- When x = 0: y = ½(0) + 2 = 0 + 2 = 2 → Point: (0, 2)
- When x = 1: y = ½(1) + 2 = 0.5 + 2 = 2.5 → Point: (1, 2.5)
- When x = 2: y = ½(2) + 2 = 1 + 2 = 3 → Point: (2, 3)
- When x = 3: y = ½(3) + 2 = 1.5 + 2 = 3.5 → Point: (3, 3.5)
- When x = 4: y = ½(4) + 2 = 2 + 2 = 4 → Point: (4, 4)

To draw: Plot these points and connect them with a straight line.

Problem 6: Draw the graph of y = -x + 3 for values of x from -3 to 3

Table of values:
- When x = -3: y = -(-3) + 3 = 3 + 3 = 6 → Point: (-3, 6)
- When x = -2: y = -(-2) + 3 = 2 + 3 = 5 → Point: (-2, 5)
- When x = -1: y = -(-1) + 3 = 1 + 3 = 4 → Point: (-1, 4)
- When x = 0: y = -(0) + 3 = 0 + 3 = 3 → Point: (0, 3)
- When x = 1: y = -(1) + 3 = -1 + 3 = 2 → Point: (1, 2)
- When x = 2: y = -(2) + 3 = -2 + 3 = 1 → Point: (2, 1)
- When x = 3: y = -(3) + 3 = -3 + 3 = 0 → Point: (3, 0)

To draw: Plot these points and connect them with a straight line.

Problem 7: Draw the graph of y = -2x + 4 for values of x from -2 to 3

Table of values:
- When x = -2: y = -2(-2) + 4 = 4 + 4 = 8 → Point: (-2, 8)
- When x = -1: y = -2(-1) + 4 = 2 + 4 = 6 → Point: (-1, 6)
- When x = 0: y = -2(0) + 4 = 0 + 4 = 4 → Point: (0, 4)
- When x = 1: y = -2(1) + 4 = -2 + 4 = 2 → Point: (1, 2)
- When x = 2: y = -2(2) + 4 = -4 + 4 = 0 → Point: (2, 0)
- When x = 3: y = -2(3) + 4 = -6 + 4 = -2 → Point: (3, -2)

To draw: Plot these points and connect them with a straight line.

Problem 8: Draw the graph of y = ¼x - 2 for values of x from -4 to 4

Table of values:
- When x = -4: y = ¼(-4) - 2 = -1 - 2 = -3 → Point: (-4, -3)
- When x = -3: y = ¼(-3) - 2 = -0.75 - 2 = -2.75 → Point: (-3, -2.75)
- When x = -2: y = ¼(-2) - 2 = -0.5 - 2 = -2.5 → Point: (-2, -2.5)
- When x = -1: y = ¼(-1) - 2 = -0.25 - 2 = -2.25 → Point: (-1, -2.25)
- When x = 0: y = ¼(0) - 2 = 0 - 2 = -2 → Point: (0, -2)
- When x = 1: y = ¼(1) - 2 = 0.25 - 2 = -1.75 → Point: (1, -1.75)
- When x = 2: y = ¼(2) - 2 = 0.5 - 2 = -1.5 → Point: (2, -1.5)
- When x = 3: y = ¼(3) - 2 = 0.75 - 2 = -1.25 → Point: (3, -1.25)
- When x = 4: y = ¼(4) - 2 = 1 - 2 = -1 → Point: (4, -1)

To draw: Plot these points and connect them with a straight line.

Final Answer:
The solutions involve creating tables of values for each equation and plotting the corresponding points on coordinate grids, then connecting them with straight lines:

1. y = x + 2: Points (-3,-1), (-2,0), (-1,1), (0,2), (1,3), (2,4), (3,5)
2. y = 2x - 1: Points (-3,-7), (-2,-5), (-1,-3), (0,-1), (1,1), (2,3), (3,5)
3. y = x - 4: Points (-3,-7), (-2,-6), (-1,-5), (0,-4), (1,-3), (2,-2), (3,-1)
4. y = 3x + 1: Points (-3,-8), (-2,-5), (-1,-2), (0,1), (1,4), (2,7), (3,10)
5. y = ½x + 2: Points (-4,0), (-3,0.5), (-2,1), (-1,1.5), (0,2), (1,2.5), (2,3), (3,3.5), (4,4)
6. y = -x + 3: Points (-3,6), (-2,5), (-1,4), (0,3), (1,2), (2,1), (3,0)
7. y = -2x + 4: Points (-2,8), (-1,6), (0,4), (1,2), (2,0), (3,-2)
8. y = ¼x - 2: Points (-4,-3), (-3,-2.75), (-2,-2.5), (-1,-2.25), (0,-2), (1,-1.75), (2,-1.5), (3,-1.25), (4,-1)