The line H has the equation y = – (½)x + 4.

Find the equation of a line that is perpendicular to line H and passes through the point(2, 3).

The equation of line H is expressed as y = – (½)x + 4. To determine the equation of a line that is perpendicular to line H and intersects at the point (2, 3), it is essential to first identify the slope of line H. The slope of line H is -½, and the slope of a line that is perpendicular to another is the negative reciprocal of the original slope. Therefore, the slope of the line we seek will be 2, as the negative reciprocal of -½ is 2.

Next, we can utilize the point-slope form of a linear equation to derive the equation of the desired line. The point-slope form is given by the equation y – y₁ = m(x – x₁), where m represents the slope and (x₁, y₁) is a point on the line. Substituting the known values, where m = 2 and the point is (2, 3), we can formulate the equation as y – 3 = 2(x – 2). Simplifying this equation will yield the final form of the line’s equation.

Upon simplifying, we find that y – 3 = 2x – 4, which leads to y = 2x – 1. Thus, the equation of the line that is perpendicular to line H and passes through the point (2, 3) is y = 2x – 1. For those seeking to enhance their understanding of such concepts, enrolling in an A Level Maths Revision Course can provide valuable insights and practice in tackling similar mathematical problems.