Hi, Sandi,
I'm not sure what the term "xt" represents. I'll change it to the following:
y - 4 = -2x
Be aware this may not be the problem you presented.
I want to rearrange this equation to standard form, to make it easier to see what it is telling us. Standard form is y = mx + b, where m is the slope and b is the y intercept, where the line crosses the y axis at x = 0.
y = -2x + 4
The slope is -2. The fun in this type of question is knowing that any line that has a negative inverse slope will be perpendicular to this line. The negative inverse of -2 is +(1/2). So an equation of the form
y = (1/2)x + b will be perpendicular, no matter the value of b. In this case, we are given one point the line must intersect, (2,3). We can use it to calculate b, since we know it satisfies the equation.
3 = (1/2)*(2) + b
b = 2
The equation that is perpendicular and goes through point (2,3) is:
y = (1/2)x + 2 (the blue line)
Bob
