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