Graphical Solution of Linear Intersection

00:00 3 marks

A graph is provided showing two straight lines: one line, L1, with the equation \(y = 2x + 1\), and another line, L2, with the equation \(y = -x + 4\). Use the graph to determine the intersection point of these lines.

(a) Identify the intersection point from the graph.

(b) For extension, explain briefly how the intersection might change if the slope of L1 were increased slightly.

Part a

3 minutes 2 marks

Question

From the provided graph, identify the coordinates of the point where the lines \(y = 2x + 1\) and \(y = -x + 4\) intersect.

Hint Hint

Hint

Look closely at the provided graph to identify the coordinates where the two lines intersect.

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Complete Answer

(1, 3)

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Part b

2 minutes 1 marks

Question

Discuss briefly how the intersection point would change if the slope of the first line (L1) were increased slightly.

Hint Hint

Hint

Consider the effect of a steeper slope for L1 on its intersection with the unchanged line L2.

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Complete Answer

The intersection x-coordinate would decrease slightly and the y-coordinate would increase slightly.

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