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Given the equation y = 4x − 3, complete the table and plot the graph.

Mathematics

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Graph of y = 4x − 3

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Key points of y = 4x − 3
Pointxy
y-intercept0−3
x-intercept0.750

Step-by-step solution

3 steps

3.3
Given the equation y=4x−3y = 4x - 3, we will complete the table by substituting each xx value into the equation to find the corresponding yy value.

  1. Calculate yy for each xx value.

    For x=−3x = -3:

    y=4(−3)−3=−12−3=−15y = 4(-3) - 3 = -12 - 3 = -15

    For x=−2x = -2:

    y=4(−2)−3=−8−3=−11y = 4(-2) - 3 = -8 - 3 = -11

    For x=−1x = -1:

    y=4(−1)−3=−4−3=−7y = 4(-1) - 3 = -4 - 3 = -7

    For x=0x = 0:

    y=4(0)−3=0−3=−3y = 4(0) - 3 = 0 - 3 = -3

    For x=1x = 1:

    y=4(1)−3=4−3=1y = 4(1) - 3 = 4 - 3 = 1

    For x=2x = 2:

    y=4(2)−3=8−3=5y = 4(2) - 3 = 8 - 3 = 5

    For x=3x = 3:

    y=4(3)−3=12−3=9y = 4(3) - 3 = 12 - 3 = 9
  2. Complete the table.

    xx-3-2-10123
    yy-15-11-7-3159
  3. Plot the graph.

    To plot the graph, you would use the coordinate pairs (x,y)(x, y) from the table:
    (−3,−15)(-3, -15), (−2,−11)(-2, -11), (−1,−7)(-1, -7), (0,−3)(0, -3), (1,1)(1, 1), (2,5)(2, 5), (3,9)(3, 9).
    Plot each of these points on a coordinate plane. Since the equation y=4x−3y = 4x - 3 is a linear equation, all these points will lie on a straight line. Draw a straight line connecting these points to represent the graph of the function.

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