Answer:
y +4 = -5/3(x -3) or y = -5/3x +1
Explanation:
You want the equation of the line with slope -5/3 through point (3, -4).
Point-slope equation
The point-slope equation for a line is ...
y -k = m(x -h) . . . . . . line with slope m through point (h, k)
For the given slope and point, your equation is ...
y -(-4) = -5/3(x -3)
y +4 = -5/3(x -3) . . . . . . point-slope equation of the line
Slope-intercept equation
This equation can be rearranged to slope-intercept form
y = -5/3x +5 -4 . . . . . eliminate parentheses, subtract 4
y = -5/3x +1 . . . . . . . collect terms
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Additional comment
The equation can also be rearranged to standard form:
5x +3y = 3
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