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Create a table and graph for the relation y = 3x − 2 for x = -2, -1, 0, 1, 2. Use the graph to find y when x = 2.5 and x when y = 7.

Mathematics

ScanSolve AI Answer

Answer

ii
5.5
3
Graph of y = 3x − 2

Use the left and right arrow keys to trace the curve, up and down to jump between key points, and plus and minus to zoom.

Key points of y = 3x − 2
Pointxy
y-intercept0−2
x-intercept0.670

Step-by-step solution

4 steps

Here's the solution for question 4.

4. (a) Create a table for the relation y=3x−2y = 3x - 2 for x=−2,−1,0,1,2x = -2, -1, 0, 1, 2.

Step 1: Calculate yy for each given xx value using the relation y=3x−2y = 3x - 2.

  • For x=−2x = -2: y=3(−2)−2=−6−2=−8y = 3(-2) - 2 = -6 - 2 = -8
  • For x=−1x = -1: y=3(−1)−2=−3−2=−5y = 3(-1) - 2 = -3 - 2 = -5
  • For x=0x = 0: y=3(0)−2=0−2=−2y = 3(0) - 2 = 0 - 2 = -2
  • For x=1x = 1: y=3(1)−2=3−2=1y = 3(1) - 2 = 3 - 2 = 1
  • For x=2x = 2: y=3(2)−2=6−2=4y = 3(2) - 2 = 6 - 2 = 4

Step 2: Form the table.

xxyy
-2-8
-1-5
0-2
11
24

4. (b) Draw the graph of the relation and use it to find:

Part i

yy when x=2.5x = 2.5

Part ii5.5

xx when y=7y = 7

(Note: As an AI, I cannot draw a graph. I will find the values by substituting into the equation, which is equivalent to reading them from a graph.)

4. (b) (i) Find yy when x=2.5x = 2.5.

  1. Substitute x=2.5x = 2.5 into the equation y=3x−2y = 3x - 2.

    y=3(2.5)−2y = 3(2.5) - 2
  2. Calculate yy.

    y=7.5−2y = 7.5 - 2 y=5.5y = 5.5

    So, yy when x=2.5x = 2.5 is 5.5\boxed{5.5}.

    4. (b) (ii) Find xx when y=7y = 7.

  3. Substitute y=7y = 7 into the equation y=3x−2y = 3x - 2.

    7=3x−27 = 3x - 2
  4. Solve for xx.

    Add 2 to both sides:

    7+2=3x7 + 2 = 3x 9=3x9 = 3x

    Divide by 3:

    x=93x = \frac{9}{3} x=3x = 3

    So, xx when y=7y = 7 is 3\boxed{3}.

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