The diagram shows the lines $y = 2x + 1$ and $7x + 4y = 28$ - OCR - GCSE Maths - Question 14 - 2018 - Paper 5
Question 14
The diagram shows the lines $y = 2x + 1$ and $7x + 4y = 28$.
The region R satisfies these inequalities.
$y \leq 2x + 1$
$7x + 4y \geq 28$
$y > 1$
By drawin... show full transcript
Worked Solution & Example Answer:The diagram shows the lines $y = 2x + 1$ and $7x + 4y = 28$ - OCR - GCSE Maths - Question 14 - 2018 - Paper 5
Step 1
Draw the line $y = 2x + 1$
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Answer
This line is positive with a slope of 2 and a y-intercept at (0, 1). Use a solid line since the inequality is less than or equal to.
Step 2
Draw the line $7x + 4y = 28$
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Answer
Rearranging this gives y=−47x+7. This line is negative with a y-intercept at (0, 7). Use a solid line since the inequality is greater than or equal to.
Step 3
Draw the line $y = 1$
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Answer
This is a horizontal line through (0, 1). Since the inequality is strictly greater than, use a broken line.
Step 4
Identify the region R
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Answer
The region R is the area that satisfies all three inequalities: below the line y=2x+1, above the line 7x+4y=28, and above the line y=1. Label the region as R on the graph.
