Answer:
Step-by-step explanation:
Solve 3x + 5y = 1 for y to obtain the slope of the given line:
5y = -3x + 1, or y = (-3/5)x + 1.
Any line perpendicular to this one has the slope which is the negative reciprocal of (-3/5): That would be 5/3.
The desired line has slope 5/3 and passes through (2, 7);
Adapt y = mx + b by substituting the known values, to find b:
7 = (5/3)(2) + b. The LCD is 3, so multiply each term by 3 to eliminate the fractional coefficient:
21 = 10 + 3b, or 11 = 3b. Then b = 11/3, and the desired equation in slope intercept form is
y = (5/3)x + 11/3
To obtain the standard form, multiply all three terms by 3 again:
3y = 5x + 11, or
5x + 11 - 3y = 0, or
5x - 3y + 11 = 0
