What is the equation that is perpendicular to the line y=2x-3 and passes through the point (-6,5)? Show all of your work.
y = 2x + 17
y = 1/2x + 8
y = -2x - 7
y = -1/2x + 2
perpendicular means the slopes are negative-reciprocals
... so the slope of the new line is the negative-reciprocal of 2 ... -1/2
using point-slope ... y - 5 = -1/2 (x + 6) ... y = -1/2 x + 2
thank you!
y = 2x + 17
Well, to find the equation of a line that is perpendicular to the line y=2x-3, we need to determine the negative reciprocal of the slope of the given line.
The given line has a slope of 2, so the negative reciprocal of 2 is -1/2.
Now, we have the slope and a point (-6, 5) that the perpendicular line must pass through.
Using the point-slope form of an equation, we get:
y - y1 = m(x - x1)
Where m is the slope and (x1, y1) is the coordinates of the given point.
Substituting in the values, we have:
y - 5 = (-1/2)(x + 6)
To simplify, we multiply both sides by 2:
2(y - 5) = -1(x + 6)
Expanding:
2y - 10 = -x - 6
Rearranging:
x + 2y = -4
So, the equation of the line that is perpendicular to y=2x-3 and passes through (-6, 5) is x + 2y = -4.
Now, let's spice things up a bit! This equation proves that even the grumpiest lines can become friends if they're perpendicular. It's a beautiful example of harmony in the math world.
To find the equation of the line that is perpendicular to the given line y = 2x - 3 and passes through the point (-6, 5), we can use the following steps:
Step 1: Determine the slope of the given line.
The given line is in slope-intercept form, y = mx + b, where m represents the slope of the line. Comparing the given equation y = 2x - 3, we can see that the slope is 2.
Step 2: Find the slope of the line perpendicular to the given line.
The slope of a line perpendicular to another line is the negative reciprocal of the slope of the given line. In this case, the slope of the perpendicular line is -1/2 (the negative reciprocal of 2).
Step 3: Use the slope-intercept form to find the equation of the perpendicular line.
We know that the perpendicular line passes through the point (-6, 5). Let's substitute this point into the slope-intercept form y = mx + b and solve for b:
5 = (-1/2)(-6) + b
5 = 3 + b
b = 5 - 3
b = 2
Now that we have the slope (-1/2) and y-intercept (b = 2), we can write the equation of the perpendicular line:
y = (-1/2)x + 2
So, the correct equation that is perpendicular to the line y = 2x - 3 and passes through the point (-6, 5) is y = (-1/2)x + 2.