Find the slope of the line perpendicular to 4 x − 5 y = 9 2 4x-5y=\frac92

we are asked to find the slope of the line that is perpendicular to four x minus five y is equal to nine over two. Now, to solve this problem, we need to understand what a perpendicular line is. And the slope of a perpendicular line, we'll call it m two, is going to be the negative reciprocal of line one, the the slope of line one. Now these lines that are in the form y equals m x plus b, we can find the slope pretty straightforward. So it's just gonna be the number in front of the x. But unfortunately, we don't have this form here. Notice that we actually have standard form, which we've seen before, the a x plus b y equals c. So So what I actually need to do is adjust my equation to get the slope intercept form. That's gonna make the slope more obvious. So what I'm going to first do is I'm going to add five y to both sides of this equation, And I'm doing that to cancel the five y's right about there. So this is gonna be that four x, and then there's nothing else there, is equal to nine halves plus, and then we have five y. Now I really need to isolate that y by itself. So I'm going to subtract the nine halves on both sides of the equal sign. That's gonna get the nine halves to cancel, giving me that five y is equal to four x minus nine halves. Now next, what I want to do is divide out this five on all on all pieces of this equation, getting the fives to cancel, leaving me with y is equal to four fifths x. And it's going to be minus, and then nine halves divided by five. Well, that's the same thing as nine over two times one fifth. So if I multiply those denominators right there, that's gonna give me nine over 10. So this is what my equation looks like, and it's the same equation that I started with. But notice now we have this in slope intercept form rather than in standard form. So now that I've found my equation, I can pretty clearly identify the slope. The slope is four fifths. So if I want to find the slope of my line that is perpendicular, that is going to be the negative reciprocal of this slope, which is gonna be negative one over four fifths. Now what I need to do is take this fraction in the the in the denominator and flip it and bring it to the top. That's gonna give me negative, and then that's gonna be five fourths. So we have now found the slope of the perpendicular line and the solution to this problem. So there's a bit more work we had to do on this problem, but the main thing you need to remember is that you need to get things into the slope intercept form to clearly see what the slope is, and then you can determine whether the lines are parallel, perpendicular, or neither based on the relationships we've discussed. So I hope you found this video helpful, and let's move on.

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Multiple Choice

Find the slope of the line perpendicular to $4 x - 5 y = \frac{9}{2}$

$\frac{4}{5}$

$\frac{9}{10}$

$- \frac{9}{2}$

$- \frac{5}{4}$

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Find the slope of the line perpendicular to 4x−5y=924x-5y=\(\frac\)92

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Find the slope of the line perpendicular to $4 x - 5 y = \frac{9}{2}$