Which of the following could be the graph of $y = -2x + 2$?
A - HSC - SSCE Mathematics Standard - Question 2 - 2022 - Paper 1
Question 2
Which of the following could be the graph of $y = -2x + 2$?
A.
B.
C.
D.
Worked Solution & Example Answer:Which of the following could be the graph of $y = -2x + 2$?
A - HSC - SSCE Mathematics Standard - Question 2 - 2022 - Paper 1
Step 1
Determine the slope and y-intercept of the equation
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Answer
The given equation is in the slope-intercept form y=mx+b, where m is the slope and b is the y-intercept.
Here, the slope m=−2 and the y-intercept b=2. This means the graph will slope downward and cross the y-axis at the point (0, 2).
Step 2
Analyze the graphs for characteristics
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Answer
To find the correct graph among the options provided (A, B, C, D), one must look for a line that:
Is a straight line (as it represents a linear equation).
Crosses the y-axis at (0, 2).
Slopes downward due to the negative slope of -2.
Step 3
Select the correct graph
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Answer
Based on the analysis, the correct option is A, as it depicts a downward-sloping line crossing the y-axis at (0, 2).
