# Match Equation to Graph Line

In this worksheet, students will match equations to their corresponding graph line.

Key stage:  KS 3

Curriculum topic:   Algebra

Curriculum subtopic:   Translate Situations/Procedures into Expressions, Formulae and Graphs

Difficulty level:

### QUESTION 1 of 10

The gradient and intercept of any line can be stated by looking carefully at its equation.

For the line with equation y = mx + c, the gradient is m and the intercept on the y-axis is c.

m is the coefficient of x when in the form y =

c is the number on its own

Example

Draw the line which is represented by y = 2x + 1

Answer

Comparing y = 2x + 1 to y = mx + c, we see that m = 2 and c = 1

Therefore, the gradient of the line (m) is 2 and the intercept (c) is 1.

This means that the line crosses the y-axis at (0, 1) and from this point we move 1 to the right and 2 up to draw the line (or 4 to the right and 8 up).

The line is shown below:

Let's tackle some questions together.

Remember, you can always refer back to this page for guidance if you need to!

Which of the given equations represents the red line shown below?

y = 2x - 3

x = 2y + 3

y = 2x + 3

y = 3x + 2

Which of the given equations represents the red line shown below?

y = 4x - 3

x = ¾y + 4

y = ½x + 4

y = ¾x + 4

Which of the given equations represents the red line shown below?

y = 8 - 2x

x = 8x - 2

y = -8x -2

y = 8x + 2

Which of the given equations represents the red line shown below?

x = 7y

x = 7

y = 7x

y = 7

Which of the given equations represents the red line shown below?

x = 8

x = 8y

y = 8x

y = 8

Which of the given equations represents the red line shown below?

x = 0

xy

y = x

y = xy

Which of the given equations represents the red line shown below?

x = 8

y = 8 - x

y = 8

y = 8xy

Which of the given equations represents the red line shown below?

y = 2x + 6

x = ½y + 4

y = ½x + 6

y = 6x + ½

Which of the given equations represents the red line shown below?

y = 2x - 6

x = 2y + 6

y = -2x + 6

y = 6 - ½x

Which of the given equations represents the red line shown below?

y = ¼x - 9

x = 9y + ¼

y = -¼x + 9

y = 9 + ¼x

• Question 1

Which of the given equations represents the red line shown below?

CORRECT ANSWER
y = 2x + 3
EDDIE SAYS
First, let's remember our important equation y = 2x +1. We can see that the gradient of the red line (m) is 2 and the y-intercept (c) is 3. This means that the line crosses the y-axis at (0, 3) and from this point we move 1 to the right and 2 up to draw the line. So, m = 2 and c = 3. Therefore the equation that represents the red line is y = 2x + 3.
• Question 2

Which of the given equations represents the red line shown below?

CORRECT ANSWER
y = ¾x + 4
EDDIE SAYS
We know that we must first write down our equation y = 2x +1. Then, we look at the graph. We can see that the gradient of the red line (m) is ¾ and the y-intercept (c) is 4. This means that the line crosses the y-axis at (0, 4) and from this point we move 1 to the right and ¾ up to draw the line. So, m = ¾ and c = 4. Therefore, the equation that represents the red line is y = ¾x + 4. How are you getting on? Is this beginning to make sense to you? Let's push on.
• Question 3

Which of the given equations represents the red line shown below?

CORRECT ANSWER
y = 8 - 2x
EDDIE SAYS
y = 2x +1 Looking at the graph we can see that the red line (m) has a gradient of -2 and the y-intercept (c) is 8. This means that the line crosses the y-axis at (0, 8) and from this point, we move 1 to the right and 2 down to draw the line. m = -2 and c = 8. y = -2x + 8 We then rearrange this formula to get y = 8 - 2x.
• Question 4

Which of the given equations represents the red line shown below?

CORRECT ANSWER
y = 7
EDDIE SAYS
y = 2x +1 Looking at the graph we can see that the red line (m) has a gradient of 0 and the y-intercept (c) is 7. This means that the line crosses the y-axis at (0, 7) and from this point, we move 1 to the right and 0 up or down, in order to plot the line. m = 0 and c = 7 y = 0x + 7 As there is no value for x, we simplify this formula to get y = 7. Are you feeling more confident?
• Question 5

Which of the given equations represents the red line shown below?

CORRECT ANSWER
x = 8
EDDIE SAYS
y = 2x +1 Looking at the graph we can see that the red line (m) has an undefined gradient, as all points on the line have the same x-intercept (8,0). We can also identify that there is no y-intercept (c). m = undefined c = 0 x = 8
• Question 6

Which of the given equations represents the red line shown below?

CORRECT ANSWER
y = x
EDDIE SAYS
y = 2x +1 Looking at the graph we can see that the red line (m) has a gradient of 1 and the y-intercept (c) is 0. This means that the line crosses the y-axis at (0, 0) and from this point, we move 1 to the right and 1 up to draw the line. m = 1 and c = 0 y = 1x + 0 y = x Look at the line on the graph. Did you notice that whatever the value of the y-coordinate is, is also the value of the x-coordinate? Great focus if you spotted that!
• Question 7

Which of the given equations represents the red line shown below?

CORRECT ANSWER
y = 8 - x
EDDIE SAYS
y = 2x +1 Looking at the graph we can see that the red line (m) has a gradient of -1 and the y-intercept (c) is 8. This means that the line crosses the y-axis at (0, 8) and from this point, we move 1 to the right and 1 down to draw the line. m = -1x and c = 8 y = -x + 8 We then rearrange this formula to get y = 8 - x.
• Question 8

Which of the given equations represents the red line shown below?

CORRECT ANSWER
y = ½x + 6
EDDIE SAYS
y = 2x +1 Looking at the graph we can see that the red line (m) has a gradient of ½ and the y-intercept (c) is 6. This means that the line crosses the y-axis at (0, 6) and from this point, we move 2 to the right and 1 up to draw the line. m = ½ and c = 6 y = ½x + 6 Keep this up, there are only 2 more questions to complete!
• Question 9

Which of the given equations represents the red line shown below?

CORRECT ANSWER
y = 6 - ½x
EDDIE SAYS
y = 2x +1 Looking at the graph we can see that the red line (m) has a gradient of -½ and the y-intercept (c) is 6. This means that the line crosses the y-axis at (0, 6) and from this point, we move 2 to the right and 1 down to draw the line. m = -½ and c = 6 y = -½x + 6 We then rearrange this to get, y = 6 - ½x
• Question 10

Which of the given equations represents the red line shown below?

CORRECT ANSWER
y = -¼x + 9
EDDIE SAYS
y = 2x +1 Looking at the graph we can see that the red line (m) has a gradient of -¼ and the y-intercept (c) is 9. This means that the line crosses the y-axis at (0, 9) and from this point, we move four to the right and 1 down to draw the line. m = -¼ and c = 9 y = -¼x + 9 That's another activity ticked off! Why not take a break before attempting another one?
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