What is equation of the line that passes through the point (3, 0) and is perpendicular to the line 2x – y = 5

2x – y = 5

Put into slope intercept form
y = 2x - 5

So the slope = 2

For a line to be perpendicular the product of the slopes of the two lines must equal -1
Therefor the slope must be -1/2

The perpendicular line in slope intercept form
y = -1/2x + b

Since the line passes through point (3, 0)
0 = -1/2(3) + b
0 = -3/2 +b
b = 3/2

Equation of perpendicular line
y = -1/2x +3/2

Write the equation in y intercept form :
2x – y = 5 =>
y = 2x - 5

If the slope of this line is 2, then the slope of a line that is perpendicular to it is -(1/2)

Now begin writing the equation for this new line
y = mx + b =>
y = -(1/2)x + b

Then they tell us that it must pass through (3,0), so plug these values in to find b:
y = -(1/2)x + b =>
0 = -(1/2)*3 + b =>
b = 3/2

Now you have the equation you're looking for:
y = -(1/2)x + (3/2)

y = - x/2 + 3/2