4. consider the following linear equation (3 marks) y = 3x + 2 a) what is the value of y when x = 7? b) what is the value of y when x = 8? c) if the value of x is increased by 1, by how much should y increase?

a) To find the value of y when x = 7, we simply substitute x = 7 into the given equation:

y = 3x + 2

y = 3*7 + 2

y = 21 + 2

y = 23

b) We do the same thing for this question, except this time we substitute x = 8 into the equation:

y = 3x + 2

y = 3*8 + 2

y = 24 + 2

y = 26

c) This is a question that relates to the gradient of the graph. The gradient is the value m in the linear equation of form y = mx + c, so in our equation of y = 3x + 2, the gradient would be 3. This is the value by which y should increase if x were to increase by 1.

We can check this by looking at our answers to the previous two questions, where the x-values differed by 1.

From a): when x = 7, y = 23

From b): when x = 8, y = 26

Thus, we can confirm that when the value of x is increased by 1, the value of y increases by 3.

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