Lines can be defined in three ways:
1) the standard form Ax + By = C
2) the slope-intercept form Y = mX + b where m is the slope of the line and b is the Y intercept
3) the point slope formula with uses a point and the slope of the line in the form Y-Y1 = m (X-X1)
The point you state is (-14, -3) so y= -3 and X = -14
"Perpendicular lines have slopes that are negative reciprocals of each other." What does that mean? It means that a pair of lines that intersect at right angles will have slopes that go in opposite directions and in opposite ways. Where line one has a slope of m, which can also be written m/1, the perpendicular line has a slope of -1/m.
The line you state is -7X - 4Y = - 4
Let's rewrite this as - 4Y = -4 + -7x (we added -7x to each side canceling it out on the left)
Not being a fan of negative numbers I would multiply both sides by (-1)
(-1) (-4Y) = -1 (-4 -7X) ----remember that + (-7) = -7
That becomes 4Y = 4 - (-7X) which equals 4Y = 4+7X or 4Y = 7X + 4
Now divide each side by 4, canceling it out on the left.
Y = (7X + 4) / 4
Now distribute the dividend to get Y = 7/4 X + 4/4 or Y = 7/4X + 1
That is a form you recognize as the Y intercept formula Y = mX + b where m = the slope
The perpaendicular line's slope will then be the negative reciprocol of 7/4 or - 4/7 (flip it and change the sign)
The point can now be used with this slope to write the equation of the line in the Point -Slope formula required to be compliant with the question.
Y - (-3) = - 4/7 {(X - (-14)}
This becomes Y + 3 = - 4/7 X - 56/7 but on standardized exams this usually is not going to be the final answer.
Subtract 3 from both sides gives you Y = - 4/7 X -56/7 - 3/1
But you must find a common denominator to subtract fractions so it is - 4/7 X - 56/7 -21/7
or Y = - 4/7 X - 35/7 or Y = - 4/7 X -5
Whew! That's a long answer and there are many short cuts that would have made this faster to explain but when you are learning algebra short cuts are a roadblock to becoming a math-master! Honor yourself and take it step by step. This is your time to become gap-free in math and anytime I can help, give me a call and schedule a session of academic coaching.
Dr. Carranza
Jane B.
Watch your signs, Doctor. The answer is actually y=4/7x+5
09/16/12