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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.
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Answer
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| Point | x | y |
|---|---|---|
| x-intercept | −1 | 0 |
| y-intercept | 0 | 1 |
Step-by-step solution
7 stepsPlease note: The equation relating and for Question 1 is not provided in the image. For the purpose of demonstrating the solution, I will assume the linear function . If the actual function is different, the calculated values and subsequent answers will change.
Part 1· 7 steps
Calculate the missing values in the table using the assumed function .
- For :
- For :
- For :
- For :
- For :
The completed table of values is:
Plot the points on graph paper.
The points to plot are: , , , , .
Draw the graph.
When plotted, these points form a straight line.
State whether the graph is linear or non-linear.
Based on the assumed function , the graph is linear.
Determine the gradient of the graph.
Using two points from the table, for example, and :
The gradient of the graph is .
Determine the y-intercept.
The y-intercept is the value of when . From the table, when , .
The y-intercept is .Determine the x-intercept.
The x-intercept is the value of when . Using the assumed function :
The x-intercept is .
Part 2
The question asks to find two integers, and , whose product is and whose sum is for a trinomial in the form .
This describes the general method for factoring a quadratic trinomial of the form . To factor it into , you need to find two integers, and , such that:
- Their product is equal to the constant term .
- Their sum is equal to the coefficient of the term, .
Since no specific trinomial (i.e., no specific values for and ) is provided in the question, specific integers and cannot be determined.
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