anaseer said:
I need help to solve this problem
Write the equation of the line through (-2,1) that is perpendicular to Y=4
I know that we to solve this problem we can use Point slope form
Y-Y1 = m(X-X1)
X-X1= (Y-Y1)m
X+2 = (4-1)/0
X = -2
Is that the right way to solve this problem
The point-slope form for the equation of a line does not ALWAYS work! Why is that so? Well, there are some lines for which the slope is UNDEFINED....that is, there is no number that can be used to represent the slope.
You should be familiar with two very special kinds of lines.....
horizontal lines have a slope of 0. The general equation of a horizontal line is y = a, where "a" is some real number.
vertical lines have UNDEFINED slope. The general equation of a vertical line is x = a, where "a" is some real number.
If you have a particular point, such as (3, 5), there is ONE vertical line through that point, and its equation is x = 3. There's ONE horizontal line through that point, and its equation is y = 5.
It might pay to take a closer look at your problem.
You are to write the equation of a line through (-2, 1) which is perpendicular to y = 4. What kind of line is y = 4? Aha! It is a horizontal line! What kind of line is perpendicular to a horizontal line? A VERTICAL line. Since the slope of a vertical line is not defined, it won't be possible to use the point-slope form for the equation of a line. However, we know that a vertical line through the point (-2, 1) will have this equation: x = -2. Done.
