Write an equation of the line that pass through point P and is parallel to the line with the given equation.
P(3,5); y=4
since y=4 is a horizontal line, you want a horizontal line that passes through P, where y=5.
Oops Spoiler alert!!
Sorry, I meant to say perpendicular instead of parallel.
The actual question is :
Write an equation of the line that pass through point P and is perpendicular to the line with the given equation.
P(3,5); y=4
well, what's the problem? A vertical line through P will have x=3. Cmon, guy, put on your thinking cap!
To find the equation of a line parallel to a given line, we need to make use of the fact that parallel lines have the same slope.
In this case, the given line has an equation of y = 4. Since this is a horizontal line, it has a slope of 0. Hence, any line parallel to it will also have a slope of 0.
Now, let's use the point-slope form of a linear equation to write the equation of the parallel line. The point-slope form is given by:
y - y1 = m(x - x1)
Where (x1, y1) is a point on the line and m is the slope.
We are given that the point P(3, 5) lies on the line. So, x1 = 3 and y1 = 5. We also know that the slope of the line is 0.
Substituting these values into the point-slope form, we get:
y - 5 = 0(x - 3)
Since the slope is 0, any number multiplied by 0 will be 0. Simplifying further, we have:
y - 5 = 0
Finally, rearranging the equation, we get:
y = 5
Therefore, the equation of the line parallel to y = 4 and passing through the point P(3, 5) is y = 5.