The line l1 passes through the point A (2, 5)

The line l1 passes through the point A (2, 5) and has gradient -1/2. Find an equation of l1, giving your answer in the form y = mx + c.  

To find the equation of the line passing through point A(2, 5) with a gradient of -1/2, we can use the point-slope form of a linear equation. The point-slope form is y – y1 = m(x – x1), where (x1, y1) is the point the line passes through, m is the gradient, and (x, y) are variables representing any point on the line. Substituting the values we have, y – 5 = -1/2(x – 2).

Next, we can simplify the equation by distributing the -1/2 on the right side. This gives us y – 5 = -1/2x + 1. To isolate y on the left side, we can add 5 to both sides of the equation. This results in y = -1/2x + 6. Therefore, the equation of the line passing through point A(2, 5) with a gradient of -1/2 is y = -1/2x + 6.

In conclusion, the equation of the line l1 passing through the point A(2, 5) with a gradient of -1/2 is y = -1/2x + 6. This equation represents a line that has a slope of -1/2 and passes through the point (2, 5) on the coordinate plane. By using the point-slope form of a linear equation and simplifying the expression, we were able to determine the equation of the line in the form y = mx + c.

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