What is an equation in point-slope form for the line perpendicular to y=2x+13 that contains (8,-4)?
y+4 = 2(x-8)
Well, looks like we need to clown around with some math here! To find the equation of a line perpendicular to y = 2x + 13, we need the slope of the perpendicular line. Since the slopes of perpendicular lines are negative reciprocals, the slope of the perpendicular line would be -1/2.
Now, let's plug in the given point (8,-4) into the point-slope form of a line: y - y₁ = m(x - x₁). Plugging in the values, we get: y - (-4) = (-1/2)(x - 8).
Time to simplify this clown show of an equation! We have y + 4 = (-1/2)x + 4, which can be rewritten as y = (-1/2)x.
So, the equation in point-slope form for the line perpendicular to y = 2x + 13 that contains the point (8,-4) is y = (-1/2)x. Voilà!
To find the equation of a line perpendicular to y = 2x + 13, we need to determine the slope of the perpendicular line first.
The given line has a slope of 2, and for a line to be perpendicular, the slopes should be negative reciprocals of each other.
So, the slope of the perpendicular line would be -1/2.
Using the point-slope form of a line, which is y - y1 = m(x - x1), where (x1, y1) is a point on the line, we can substitute the given point (8, -4) and the slope (-1/2) to find the equation of the line.
The equation in point-slope form for the line perpendicular to y = 2x + 13 that contains (8,-4) is:
y - (-4) = (-1/2)(x - 8)
Simplifying this equation gives:
y + 4 = (-1/2)x + 4
Finally, we can rearrange the equation to slope-intercept form (y = mx + b):
y = (-1/2)x + 4 - 4
So, the equation of the line perpendicular to y = 2x + 13 that contains the point (8, -4) is:
y = (-1/2)x.
To find an equation in point-slope form for the line perpendicular to y=2x+13 and containing the point (8,-4), we need to use the following steps:
Step 1: Find the slope of the given line.
The equation is y=2x+13, which is in the slope-intercept form y=mx+b. In this equation, the coefficient of x (m) represents the slope. So, the slope of the given line y=2x+13 is 2.
Step 2: Determine the slope of the line perpendicular to the given line.
A line that is perpendicular to another line has a slope that is the negative reciprocal of the original line's slope. So, the slope of the line perpendicular to y=2x+13 would be -1/2.
Step 3: Use the slope and the given point to write the equation in point-slope form.
The point-slope form of a linear equation is y - y1 = m(x - x1), where (x1, y1) is a known point on the line, and m is the slope.
Using the given point (8,-4) and the perpendicular slope of -1/2, plug the values into the point-slope form equation:
y - (-4) = -1/2(x - 8)
Simplifying the equation:
y + 4 = -1/2x + 4
Rearranging the equation to the standard form:
y = -1/2x + 4 - 4
Simplifying further:
y = -1/2x
Therefore, the equation in point-slope form for the line perpendicular to y=2x+13 and containing the point (8,-4) is y = -1/2x.