C#

-5 to 15 = 0 to 20 is 21 'points'
0 to 29 is 30 pixels

thus

Y = ((y + 5) / 21 * 30) // transform 'points' to pixels
Y' = 29 - Y             // flip down to up

Y = ((y + 5) * 30) / 21 // transform 'points' to pixels

double Y = ((y + Math.Abs(dMin)) * (dHeight - 1)) / (dMax - dMin);
Y = dHeight - 1 - Y;

//lst.Add(-5);
lst.Add(0);
lst.Add(3);
lst.Add(7);
lst.Add(10);
//lst.Add(15);

List<double> lst = new List<double>();

lst.Add(0);
lst.Add(3);
lst.Add(7);
lst.Add(10);

double dMin = lst.Min();
double dMax = lst.Max();

double dHeight = 30;

//double y = 0; // 29 is correct
double y = 10; // 1.72 not correct

double Y = ((y + Math.Abs(dMin)) * dHeight) / (dMax - dMin + 1);
Y = dHeight - 1 - Y;

System.Diagnostics.Debug.WriteLine(Y);

// version two, passes test of reversing the two sample ranges defined here
private Dictionary<int, int> MapRangeValues(bool flipSign, List<int> sourceRange, List<int> mapToRange)
{
    var dctTransform = new Dictionary<int, int>();

    double ratio = Convert.ToDouble(mapToRange.Max() - mapToRange.Min()) / (sourceRange.Max() - sourceRange.Min());

    int offset = mapToRange[0] - sourceRange[0] + 1;

    foreach (var sInt in sourceRange)
    {
        int val = Convert.ToInt32(ratio*sInt) + offset;
            //(sInt + offset));

        if (flipSign)
        {
            val = mapToRange.Max() - val - 1;
        }
        else
        {
            val--;
        }

        dctTransform.Add(sInt, val);
    }

    return dctTransform;
}

// some test data
private List<int> DataRange = Enumerable.Range(-5, 21).ToList();

private List<int> ControlRange = Enumerable.Range(0, 30).ToList();

// requires two TextBoxes on a Form ...
private void testTheSucker()
{
    textBox1.Clear();
    textBox2.Clear();

    var result1 = MapRangeValues(true, DataRange, ControlRange);

    var result2 = MapRangeValues(false, ControlRange, DataRange);

    foreach (var kvp in result1)
    {
        textBox1.Text += string.Format("{0}\t{1}\r\n", kvp.Key, kvp.Value);
    }

    foreach (var kvp in result2)
    {
        textBox2.Text += string.Format("{0}\t{1}\r\n", kvp.Key, kvp.Value);
    }
}