Math Problem?

Question

What is the equation of the line parallel to AB passing through C?
Write your answer in both slope-int. and standard forms.

Points: A(1,4) B(3,7) C(-1,5)

Answer 1

OK, first find line AB. Actually, check that. You want to find the slope of the line AB. Since m = Δy/Δx, plug in your coordinates for A and B and go...

m = (7-4)/(3-1)
m = 3/2

Now, you can use the point-slope formula to find the line passing through point C... y-y1 = m (x-x1)
y-5 = (3/2)(x+1)
y-5 = 3x/2 + 3/2
y = 3x/2 + 13/2

So, your slope-intercept form will be y=mx+b
y=(3/2)x + 6.5
Since Standard form presents in the form Ax+By=C,
y = 3x/2 + 13/2
2y = 3x + 13
3x + -2y = -13

Answer 2

Simple!

Let the equation of the line be y = mx + c.

Since its parallel to AB, it would have the same slope as AB.

Slope of AB = (7-4)/(3-1) = 3/2 = 1.5

Now substitute the co-ordinates of C to get the value of c.

c = y- mx = 5 - (1.5* -1) = 6.5

The equation of the line is y = 1.5x + 6.5.

Convert it to other forms!

Answer 3

Dude first off all you need to give more info like if its passing through a tangent or a chord.

But the general formula to finding a straight line is by first finding the gradient of line C by using the co-ordinates of A and B using mid point theory

next use th reciprocal of the gradient you found in the following way:

(y1-y2) +m(x1-x2)

y1 and y2 are the y co-rdinates or either (a or b) and C respectively and x1 and x2 are the x co-ordinates of the same
M= the reciprocal of the gradient by the way.

GOOD LUCK!!

Answer 4

DO YOUR OWN HOMEWORK!!! Really, this late in the year, you should know what you're doing.