Write the equation parallel to y=-2 (3,6) Equation perpendicular to y=-5 (4,7)
To find the equation parallel to y = -2 passing through the point (3, 6), we first need to identify the slope of the given line. Since the equation is y = -2, the slope is 0, because the line is horizontal.
When a line is parallel to another line, their slopes are equal. Therefore, we want to find a line parallel to y = -2, so our new line should also have a slope of 0.
To write the equation, we use the point-slope form, which is: y - y₁ = m(x - x₁), where (x₁, y₁) represents the coordinates of a point on the line, and m is the slope.
Using the point (3, 6) and the slope m = 0, the equation becomes:
y - 6 = 0(x - 3)
Simplifying,
y - 6 = 0
Finally, we rewrite the equation in slope-intercept form (y = mx + b):
y = 0 + 6
Therefore, the equation parallel to y = -2 passing through the point (3, 6) is y = 6.
Now, let's find the equation perpendicular to y = -5 passing through the point (4, 7).
First, we need to determine the slope of the given line. Since the equation is y = -5, the slope is also 0, as the line is horizontal.
The slope of a perpendicular line is the negative reciprocal of the slope of the given line. Therefore, the slope of the perpendicular line is 1/0, which is undefined.
When the line is vertical, the equation takes the form x = a, where a represents the x-coordinate of any point on the line.
Using the point (4, 7), the equation perpendicular to y = -5 passing through the point (4, 7) is:
x = 4
Thus, the equation perpendicular to y = -5 passing through the point (4, 7) is x = 4.