Question

Write an equation of the line containing the point (3,5) and perpendicular to the line 4x-3y=5

Answer 1

Answer:

Step-by-step explanation:

In order to write the equation of the line perpendicular to the given line, we first have to know what the slope of the given line is, and there's no way to tell by looking at it in its current form, which is standard. We need to solve that equation for y to determine the slope of that line. Solving for y:

$-3y=-4x+5$ and

3y = 4x - 5 (just change all the signs so our y term isn't negative anymore...yes, you're "allowed" to do that!) and

$y=\frac{4}{3}x-\frac{5}{3}$ So we can see now that the slope of this line is 4/3. That means that the perpendicular slope is -3/4. Passing through the given point (3, 5):

$y-5=-\frac{3}{4}(x-3)$* and

$y-5=-\frac{3}{4}x+\frac{9}{4}$ and

$y=-\frac{3}{4}x+\frac{9}{4}+\frac{20}{4}$ so

$y=-\frac{3}{4}x+\frac{29}{4}$** and, in standard form:

4y = -3x + 29 and

3x + 4y = 29***

* : point-slope form

** : slope-intercept form

*** : standard form