What Is the Slope of the Line Described by the Equation 3x - 15y + 7 = 0?

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To find the slope of the line described by the equation 3x - 15y + 7 = 0, the equation can be rearranged into slope-intercept form (y = mx + b). By isolating y, the equation becomes y = 0.2x + 0.47, indicating that the slope (m) is 0.2. The transformation involved dividing through by 15 to simplify the equation. The final slope can also be expressed as 1/5 when simplified from the fraction 3/15. Understanding this process is essential for graphing linear functions accurately.
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Homework Statement


find the linear fuction ( in swedish its called the riktningskoefficient i think ,dunno if there the same thing am taking the text from a swedish book and translating to english) for the stright line 3x-15y+7=0


Homework Equations


Am unsure on how to proceed but I think i should divid all the turns by 15 or 3 to get ether 3x or 15y to just x or y, and seeing as its a graph getting y alone would have to be the easyest way to go



The Attempt at a Solution



3x-15y+7=0
15y=3x+7
y=0.2x+0.47
 
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y=(3/15)x+7/15 is how I would leave it.
 

Thread 'Family of lines that are at a distance of 5 from the origin'

I picked up this problem from the Schaum's series book titled "College Mathematics" by Ayres/Schmidt. It is a solved problem in the book. But what surprised me was that the solution to this problem was given in one line without any explanation. I could, therefore, not understand how the given one-line solution was reached. The one-line solution in the book says: The equation is ##x \cos{\omega} +y \sin{\omega} - 5 = 0##, ##\omega## being the parameter. From my side, the only thing I could...
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