Writing equations of perpendicular lines (example 2)
About this video
The video finds the equation of a line perpendicular to a line with slope -2/5 that passes through the point (2, 8). It uses the negative reciprocal to get a slope of 5/2, writes the line in point-slope form, then rearranges it into slope-intercept form, y = 5/2 x + 3.
You'll be able to
- find the slope of a line perpendicular to a given line using the negative reciprocal.
- write the equation of a line in point-slope form from a slope and a point.
- convert a point-slope equation into slope-intercept form.
Key words
- perpendicular
- Two lines are perpendicular when they meet at a right angle; their slopes are negative reciprocals of each other.
- negative inverse (negative reciprocal)
- Flip a fraction upside down and change its sign, so -2/5 becomes 5/2.
- point-slope form
- An equation of a line written as y - y1 = m(x - x1), using slope m and a point (x1, y1).
- slope-intercept form
- An equation of a line written as y = mx + b, where m is the slope and b is the y-intercept.
Transcript
- [Instructor] Find the equation of a line perpendicular to this line that passes to the point two comma eight. So this first piece of information that it's perpendicular to that line right over there. What does that tell us? Well if it's perpendicular to this line, it's slope has to be the negative inverse of two-fifths.
So its slope, the negative inverse of two-fifths, the inverse of two-fifths is five. Let me do it in a better color. A nicer green. If this lines slope is negative two-fifths, the equation of the line we have to figure out that's perpendicular, the slope is going to be the inverse.
So instead of two-fifths, it's gonna be five halves. And instead of being a negative, it's going to be a positive. So this is the negative inverse of negative two-fifths, right. You take the negative sign, it becomes positive. You swap the five and the two, you get five halves.
So that is going to have to be our slope. And we can actually use the point slope form right here. It goes through this point right there. So let's use point slope form. Y minus this Y value which has to be on the line. Is equal to our slope, five halves times X minus this X value.
The X value when Y is equal to eight. And this is the equation of the line in point slope form if you wanna put it in slope intercept form. You can just do a little bit of algebra. Algebraic manipulation. Y minus eight is equal to let's distribute the five halves.
So five halves X minus five halves times two is just five. And then add eight to both sides. You get Y is equal to five halves X. Add eight to negative five. So plus three. And we are done.
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