Question

Write the equation of the line that passes through the points (1,5) and (9,1). Put your answer in fully reduced point-slope form, unless it is a vertical or horizontal line.

Answer 1

Answer:

These are tough, you need a strategy and the formula to go with it, use the point slope formula { y-y1=m(x-x1)  } where m = slope and (x1,y1 ) are the points from one of the given points.

find m .. then plug in your point to your formula ... as follows

Step-by-step explanation:

given: (x1,y1)=(1,5)     and   (x2,y2)=(9,1)

m = y2-y2 /  x2- x1

m = 1-5 / 9-1

m = -4 / 8

m = -1/2

use  the give point (1,5) and plug in with the slope  you just solved for

y-y1 = m (x-x1)

y-5 = -1/2 (x -1)

y-5 = -1/2x + 1/2

y = -1/2x +5 1/2

above is the slope intercept form  y = mx +b   :)  see?

as a side note.. notice that either point (1,5) or (9,1) gets the same slope intercept equation? when it's plugged in,  so just use which ever one seems easier to you.

Answer 2

Answer:

This is the point-slope form.

$y - 5 = - \frac{1}{2} (x - 1)$

Step-by-step explanation:

Let's find the slope first. Remember that:

$m = \frac{y_2 - y_1}{x_2 - x_1}$

Let's find the slope now.

$m = \frac{1 - 5}{9 - 1} = \frac{ - 4}{ \: \: \: 8} = - \frac{1}{2}$

-----------------------------------------------------------

Done. Remember that point-slope form is:

$y - y_1 = m(x - x_1)$

All we have to do now is plug in.

$y - 5 = - \frac{1}{2} (x - 1)$

And we are now done!