What is the equation of a parallel line?

AI Thread Summary
To find the equation of a parallel line to 3y + 4x = 6 that passes through the point F(1,7), first convert the equation to slope-intercept form, yielding y = -4/3x + 2. The slope of the original line is -4/3, which means the parallel line will also have this slope. Using the point-slope form of the equation with the point F(1,7), the equation of the parallel line can be derived. It's essential to maintain clarity in notation to avoid confusion, especially with fractions. The discussion emphasizes the importance of understanding slopes when determining equations of parallel lines.
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Homework Statement



find the equation of the straight line which is parallel to the line 3y+4x=6 and passes through the point F (1,7)

Homework Equations





The Attempt at a Solution


3y= -4x + 6

y= -4/3x + 2


im not sure what I am doing...im i on the right track
 
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Be careful with your notation. Many people would interpret -4/3x as -4/(3x) but you mean (-4/3)x.

Okay, so far you have found the "slope-intercept" formula for the line. What is the slope of the line? Of course, a parallel line will have the same slope.
 

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