Find the slope and the y-intercept of the line. This example is written in function notation, but is still linear. As shown above, you can still read off the slope and intercept from this way of writing it. We can get down to business and answer our question of what are the slope and y-intercept.
Slopes of parallel and perpendicular lines Video 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. 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. 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.
And we are done.When we subtract two vectors, we just take the vector that’s being subtracting, reverse the direction and add it to the first vector. This is because the negative of a vector is that vector with the same magnitude, but has an opposite direction (thus adding a vector and its negative results in a zero vector)..
Note that to make a vector negative, you can just . Example 6: Find an equation of the line that passes through the point (0, -3) and is perpendicular to the line -x + y = 2.
Solution to Example 6: Let m 1 be the slope of the line whose equation is to be found and m 2 the slope of the given line. Rewrite the given equation in slope intercept form and find its slope. y = x + 2 slope m 2 = 1 ; Two lines are perpendicular .
Definiton of the equation of a straight line, in 'slope and intercept' form: y = mx+b. After completing this tutorial, you should be able to: Find the slope given a graph, two points or an equation. Write a linear equation in slope/intercept form.
Given the line 2x – 3y = 9 and the point (4, –1), find lines, in slope-intercept form, through the given point such that the two lines are, respectively: (a) parallel to the given line, and (b) perpendicular to it.
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