Final answer:
To write the standard form of the equation of a line given the point (-5, -3) and slope 3/5, substitute into the point-slope form, simplify, and rearrange to -3x + 5y = 0.
Step-by-step explanation:
To write the standard form of the equation of a line through a given point with a given slope, we can use the point-slope form of a linear equation, which is y - y1 = m(x - x1), where (x1, y1) is a point on the line, and m is the slope of the line.
The point given is (-5, -3), and the slope is 3/5. Substituting these values into the point-slope form gives us:
y - (-3) = (3/5)(x - (-5))
Simplify and distribute:
y + 3 = (3/5)x + 3
To write this in standard form, Ax + By = C, where A, B, and C are integers, we need to get rid of the fraction and move all terms to one side of the equation:
Multiply every term by 5 to eliminate the fraction:
5y + 15 = 3x + 15
Then move all terms involving variables to one side and constant terms to the other side:
-3x + 5y = 0
This is the standard form of the equation of the line.