The graphs of $x = -3$ and $y = -x$ are drawn on the grid - OCR - GCSE Maths - Question 15 - 2023 - Paper 5
Question 15
The graphs of $x = -3$ and $y = -x$ are drawn on the grid.
The region R satisfies the following inequalities.
$x < -3$
$y \leq -x$
$y - 1 > \frac{1}{2} x$
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Worked Solution & Example Answer:The graphs of $x = -3$ and $y = -x$ are drawn on the grid - OCR - GCSE Maths - Question 15 - 2023 - Paper 5
Step 1
Draw the line for $y - 1 > \frac{1}{2} x$
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Answer
To satisfy the inequality y−1>21x, rearrange it to get y>21x+1. This is a line with a gradient of 21 and a y-intercept of 1. Draw this dashed line on the graph to represent that any point above this line is part of region R.
Step 2
Identify and label zone R
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Answer
The region R is the area on the graph satisfying:
x<−3: This is the region to the left of the vertical line x=−3.
y≤−x: This area is below the line y=−x.
y>21x+1: This area is above the line I just drew.
Thus, the intersection of these three regions is the correct region R, which should be clearly marked on the graph.
