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
x < -3
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Answer
This inequality represents a vertical line at x=−3, with the region to the left of this line being shaded. Therefore, any point satisfying this inequality must have an x-coordinate less than -3.
Step 2
y ≤ -x
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Answer
The line y=−x has a negative slope and passes through the origin. The region is below this line, including the line itself, which represents solutions to this inequality.
Step 3
y - 1 > \frac{1}{2} x
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Answer
Rearranging this gives us y>21x+1. This represents a line with a positive slope of rac{1}{2}. The region is above this line.
Step 4
Draw one more line to find and label region R
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Answer
To complete the representation of the region R, you can draw the line x=−3 and also add the line y=−x in broken format to indicate it's an inequality included region. Shade the area left of x=−3 and below the line y=−x, also above the line y=21x+1. Label the shaded area as 'R'.
