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
Identify the Equation
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Answer
The given equation is a linear equation in slope-intercept form:
y = mx + b, where m is the slope and b is the y-intercept.
From the equation y=−2x+2, we can identify:
Slope (m) = -2
Y-intercept (b) = 2
Step 2
Determine the Y-Intercept
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Answer
The y-intercept occurs where the line crosses the y-axis. For the equation y=−2x+2, when x = 0:
exty−intercept:exty=−2(0)+2=2
Thus, the line crosses the y-axis at the point (0, 2).
Step 3
Determine the Slope
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Answer
The slope of -2 indicates that for every unit increase in x, y decreases by 2 units. This means the line will slant downwards from left to right.
Step 4
Evaluate the Graph Options
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Answer
Now we need to assess each graph option:
Graph A: Starts from (0, 2) and slopes downwards, which matches the characteristics of our equation.
Graph B: Either does not cross the y-axis at (0, 2) or slopes in the wrong direction.
Graph C: Similar issues as Graph B.
Graph D: Does not correspond to our equation's y-intercept.
The correct graph representation for y=−2x+2 is therefore A.
