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To determine the equation of a line that is parallel to line F, which is represented by the equation y = 2x + 5, we first need to recognise that parallel lines share the same slope. In this case, the slope of line F is 2. Therefore, any line parallel to line F will also have a slope of 2.
Next, we need to find the specific equation of the parallel line that passes through the point G(4, 1). To do this, we can utilise the point-slope form of a linear equation, which is expressed as y – y₁ = m(x – x₁), where m represents the slope and (x₁, y₁) is a point on the line. Substituting the known values, we have m = 2, x₁ = 4, and y₁ = 1. This leads us to the equation y – 1 = 2(x – 4).
By simplifying this equation, we can derive the standard form of the line. Expanding the equation gives us y – 1 = 2x – 8, which can be rearranged to y = 2x – 7. Thus, the equation of the line that is parallel to line F and passes through the point G(4, 1) is y = 2x – 7. For those looking to deepen their understanding of such concepts, enrolling in an A Level Maths Revision Course can provide valuable insights and practice.
