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# Writing equations of perpendicular lines (example 2)

Sal finds the equation of a line perpendicular to a line given in slope-intercept form that passes through a specific point.

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• why did you substract values of point from y and x in equation?
can you explain, how it works?
• I do not understand exactly what I should do . My teacher told me that we would flip like you said -2/5 to 5/2 . I don't understand why you have to flip the fraction.
• The inverse of -2/5 is 5/2, as you know. Perpendicular lines have inverse slopes.
• Do you HAVE to use point slope form here?
• No, you don't have to use point slope.
You could use the slope intercept form, y = mx +b. We know from the video that m=5/2. You can figure out what b is by setting x=2 and y=8.
• Couldn't you just substitute the points given into the equation, then you would reciprocate and change the sign of the slope..... correct me if I'm wrong cause point slope just seems alot more confusing
• No because the point is not necessarily on the original line. If you assume they are on the original line, then you would get the wrong value for y intercept.
Lets try: say y = 2x + 3 and you want a perpendicular that goes through (-2,4)
Rather than point slope, I will use the slope intercept equation and substitute
y = =1/2 x + b, so 4 = -1/2 (-2) + b, 4 = 1 + b, b = 3 and your perpendicular equation is y = -1/2 x + 3
If I tried to do your suggestion of just substituting, I would get 4 = 2 (-2) + 3 so 4=1 which does not make sense If you substituted looking for b 4 = 2 (-2) + b, so b = 8 which is different from the correct equation above.
• How would you write and equation for a perpendicular line x= -3, through (2,1)?
• x= lines are vertical, so a perpendicular line would be a horizontal line in the form y = #. Since the y intercept of the equation must be 1, the answer is y = 1.
• What is point-slope form?
• If we have a point on the line with coordinates (y₁, x₁), and the line has a slope of m, the point-slope form of the line is y-y₁=m(x-x₁)
• What is the meaning of that : "Lines with undefined slopes have the form of x = c, where c is the x-intercept."?
• If a line has an undefined slope, that's because the "change in x" that is the denominator of the slope equals zero.
Since there's no "change in x" (but y can take on any value), the line is vertical.
In order to write its equation, all we need to know is where it crosses the X-axis and we call that point c, giving us the equation x = c.
So, for example, x = -4 would be a vertical line crossing the X-axis at -4
and x = 0 would be a vertical line coinciding with the Y-axis.
Hope this helps.
• at , what is the slope of the line perpendicular to 2x+y=5