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Calculate the missing values in the table. Plot the points on graph paper. Draw the graph. State whether the graph is linear or non-linear. Determine the gradient of the graph. Determine the y-intercept. Determine the x-intercept.

Mathematics

ScanSolve AI Answer

Answer

1
1
-1
Graph of y = x + 1

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 = x + 1
Pointxy
x-intercept−10
y-intercept01

Step-by-step solution

7 steps

Please note: The equation relating xx and yy for Question 1 is not provided in the image. For the purpose of demonstrating the solution, I will assume the linear function y=x+1y = x + 1. If the actual function is different, the calculated values and subsequent answers will change.

Part 1· 7 steps

  1. Calculate the missing values in the table using the assumed function y=x+1y = x + 1.

    • For x=−2x = -2: y=−2+1=−1y = -2 + 1 = -1
    • For x=−1x = -1: y=−1+1=0y = -1 + 1 = 0
    • For x=0x = 0: y=0+1=1y = 0 + 1 = 1
    • For x=1x = 1: y=1+1=2y = 1 + 1 = 2
    • For x=2x = 2: y=2+1=3y = 2 + 1 = 3

    The completed table of values is:

    x−2−1012y−10123\begin{array}{|c|c|c|c|c|c|} \hline x & -2 & -1 & 0 & 1 & 2 \\ \hline y & -1 & 0 & 1 & 2 & 3 \\ \hline \end{array}
  2. Plot the points on graph paper.

    The points to plot are: (−2,−1)(-2, -1), (−1,0)(-1, 0), (0,1)(0, 1), (1,2)(1, 2), (2,3)(2, 3).

  3. Draw the graph.

    When plotted, these points form a straight line.

  4. State whether the graph is linear or non-linear.

    Based on the assumed function y=x+1y = x + 1, the graph is linear.

  5. Determine the gradient of the graph.

    Using two points from the table, for example, (0,1)(0, 1) and (1,2)(1, 2):

    m=y2−y1x2−x1=2−11−0=11=1m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{2 - 1}{1 - 0} = \frac{1}{1} = 1

    The gradient of the graph is 1\boxed{1}.

  6. Determine the y-intercept.

    The y-intercept is the value of yy when x=0x = 0. From the table, when x=0x=0, y=1y=1.
    The y-intercept is 1\boxed{1}.

  7. Determine the x-intercept.

    The x-intercept is the value of xx when y=0y = 0. Using the assumed function y=x+1y = x + 1:

    0=x+10 = x + 1 x=−1x = -1

    The x-intercept is −1\boxed{-1}.

Part 2

The question asks to find two integers, rr and ss, whose product is cc and whose sum is bb for a trinomial in the form x2+bx+cx^2 + bx + c.

This describes the general method for factoring a quadratic trinomial of the form x2+bx+cx^2 + bx + c. To factor it into (x+r)(x+s)(x+r)(x+s), you need to find two integers, rr and ss, such that:

  • Their product r×sr \times s is equal to the constant term cc.
  • Their sum r+sr + s is equal to the coefficient of the xx term, bb.

Since no specific trinomial (i.e., no specific values for bb and cc) is provided in the question, specific integers rr and ss cannot be determined.

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