GCSE OCR Maths Dimensions: On the same grid, draw the graph

On the same grid, draw the graph of $y = 2x - 6$ for $-1 \leq x \leq 5$ - OCR - GCSE Maths - Question 8 - 2019 - Paper 1

Question 8

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On the same grid, draw the graph of $y = 2x - 6$ for $-1 \leq x \leq 5$. Use your graphs to solve the equation $x^2 - 4x + 1 = 2x - 6$. Give your answers to 1 deci... show full transcript

Worked Solution & Example Answer:On the same grid, draw the graph of $y = 2x - 6$ for $-1 \leq x \leq 5$ - OCR - GCSE Maths - Question 8 - 2019 - Paper 1

Step 1

Draw the graph of $y = 2x - 6$

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Answer

To draw the graph of the equation $y = 2x - 6$ for the range $-1 \leq x \leq 5$ , we first calculate the coordinates for the endpoints:

When $x = -1$ :
$y = 2(-1) - 6 = -8$
So the point is $(-1, -8)$ .
When $x = 5$ :
$y = 2(5) - 6 = 4$
So the point is $(5, 4)$ .

We can plot these points on the graph and draw a straight line through them as this is a linear equation.

Step 2

Use your graphs to solve the equation $x^2 - 4x + 1 = 2x - 6$

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Answer

First, we rearrange the equation: $x^2 - 4x + 1 - 2x + 6 = 0$ which simplifies to: $x^2 - 6x + 7 = 0$

Next, to solve this equation graphically, we plot the graphs of $y = x^2 - 4x + 1$ and $y = 2x - 6$ on the same grid. The solutions to the equation will be the x-coordinates where the two graphs intersect.

Upon analyzing the graph, we find the intersection points approximately at:

$x \approx 2.5$
$x \approx 3.5$

Thus, the answers to 1 decimal place are approximately:

$x = 2.5$ or $x = 3.5$ .

On the same grid, draw the graph of $y = 2x - 6$ for $-1 \leq x \leq 5$ - OCR - GCSE Maths - Question 8 - 2019 - Paper 1

Worked Solution & Example Answer:On the same grid, draw the graph of $y = 2x - 6$ for $-1 \leq x \leq 5$ - OCR - GCSE Maths - Question 8 - 2019 - Paper 1

Draw the graph of $y = 2x - 6$

Use your graphs to solve the equation $x^2 - 4x + 1 = 2x - 6$

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