The graphs of $y = x$ and $y = -2$ are drawn on the grid - OCR - GCSE Maths - Question 17 - 2020 - Paper 1
Question 17
The graphs of $y = x$ and $y = -2$ are drawn on the grid.
The region R satisfies the following inequalities.
$y > 2$
$y \leq x$
$y < 4 - 2x$
By drawing one ... show full transcript
Worked Solution & Example Answer:The graphs of $y = x$ and $y = -2$ are drawn on the grid - OCR - GCSE Maths - Question 17 - 2020 - Paper 1
Step 1
y > 2
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Answer
This inequality indicates that the region lies above the line y=2. We draw a dashed horizontal line at y=2 since this is a strict inequality.
Step 2
y \leq x
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Answer
This line represents y=x. The region lies below or on this line. We draw a solid line along y=x.
Step 3
y < 4 - 2x
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Answer
We can rearrange the inequality to find its intercepts. Setting y=4−2x, the y-intercept occurs when x=0, giving y=4. The x-intercept occurs when y=0, giving 2x=4, so x=2. We draw a dashed line from (0, 4) to (2, 0). This represents the region below this line.
Step 4
Region R
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Answer
The region R is now defined as the area above the line y=2, below the line y=x, and below the line y=4−2x. All these inequalities will help identify a triangular area on the graph.
