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.
$x < -3$
$y \, \leq \, -x$
$y - 1 > \frac{1}{2} x$
B... show full transcript
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
96%
114 rated
Only available for registered users.
Sign up now to view full answer, or log in if you already have an account!
Answer
This inequality indicates that the region is to the left of the vertical line x=−3. You would shade the area to the left of this line.
Step 2
y ≤ -x
99%
104 rated
Only available for registered users.
Sign up now to view full answer, or log in if you already have an account!
Answer
This inequality indicates that the region is below or on the line y=−x. This line has a negative slope and passes through the origin, and you would shade the area below this line.
Step 3
y - 1 > \frac{1}{2} x
96%
101 rated
Only available for registered users.
Sign up now to view full answer, or log in if you already have an account!
Answer
Rearranging this inequality gives us y>21x+1. This line will be drawn with a positive slope of 21 and a y-intercept at 1. You would shade above this line.
Step 4
Final line to draw and label region R
98%
120 rated
Only available for registered users.
Sign up now to view full answer, or log in if you already have an account!
Answer
To correctly identify the region R, draw the line y=21x+1 as a solid line, indicating the boundary above which the region lies. Label the final region R that satisfies all the inequalities: the area that is to the left of x=−3, below y=−x, and above y=21x+1.
